Electrostatics and Electrical Fields - MCAT Chemical and Physical Foundations of Biological Systems
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Two charges Q1 and Q2 are held stationary 1 m away from each other. The magnitude of charge of Q2 is twice that of Q1. A positive point charge A is placed directly in the middle of the two charges (Q1 and Q2). What is the ratio of the net force on charge A when Q1 and Q2 are both negative over the net force on charge A when Q1 is negative and Q2 is positive?
Two charges Q1 and Q2 are held stationary 1 m away from each other. The magnitude of charge of Q2 is twice that of Q1. A positive point charge A is placed directly in the middle of the two charges (Q1 and Q2). What is the ratio of the net force on charge A when Q1 and Q2 are both negative over the net force on charge A when Q1 is negative and Q2 is positive?
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For this problem we must understand Coulomb's Law. The force on charge A will be dircetly affected by the charge of Q1 and Q2. Q1 and Q2 are both negative, they will both attract charge A, and the net force will be reduced as they pull in opposite directions. Switching Q2 to a positive charge will result in a repulsive force on charge A which will be in the same direction as the attractive force between Q1 and A.
For this problem we must understand Coulomb's Law. The force on charge A will be dircetly affected by the charge of Q1 and Q2. Q1 and Q2 are both negative, they will both attract charge A, and the net force will be reduced as they pull in opposite directions. Switching Q2 to a positive charge will result in a repulsive force on charge A which will be in the same direction as the attractive force between Q1 and A.
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Two point charges, Q1 and Q2, are placed on the x-axis. Q1 is placed at x = 0m and Q2 at x = 1m. If a positive charge, Q3, is placed on the x-axis at x = 0.25m, it experiences a net electric force of 0. Which of the following could be determined based on this observation?
Two point charges, Q1 and Q2, are placed on the x-axis. Q1 is placed at x = 0m and Q2 at x = 1m. If a positive charge, Q3, is placed on the x-axis at x = 0.25m, it experiences a net electric force of 0. Which of the following could be determined based on this observation?
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In order for there to be 0 net force on Q3, the forces from Q1 and Q2 must be in opposite directions. So Q1 and Q2 must either be both attracting Q3 or both repelling Q3 (that is, Q1 and Q2 are either both negative or both positive).
Also, since these forces must have equal magnitude in order to cancel, such that 
, where 
is the magnitude of force between Q1 and Q3, and similarly for 
. Recalling Coulomb’s law for electric force, 
and 
(where Q1, Q2, and Q3 are the magnitudes of the respective charges). Since 
, it must also be true that 
for the two fractions to have the same value. So, Q2 must have a greater magnitude than Q1.
In order for there to be 0 net force on Q3, the forces from Q1 and Q2 must be in opposite directions. So Q1 and Q2 must either be both attracting Q3 or both repelling Q3 (that is, Q1 and Q2 are either both negative or both positive).
Also, since these forces must have equal magnitude in order to cancel, such that
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Electronegativity is an important concept in physical chemistry, and often used to help quantify the dipole moment of polar compounds. Polar compounds are different from those compounds that are purely nonpolar or purely ionic. An example can be seen by contrasting sodium chloride, NaCl, with an organic molecule, R-C-OH. The former is purely ionic, and the latter is polar covalent.
When comparing more than one polar covalent molecule, we use the dipole moment value to help us determine relative strength of polarity. Dipole moment, however, is dependent on the electronegativity of the atoms making up the bond. Electronegativity is a property inherent to the atom in question, whereas dipole moment is a property of the bond between them.
For example, oxygen has an electronegativity of 3.44, and hydrogen of 2.20. In other words, oxygen more strongly attracts electrons when in a bond with hydrogen. This leads to the O-H bond having a dipole moment.
When all the dipole moments of polar bonds in a molecule are summed, the molecular dipole moment results, as per the following equation.
Dipole moment = charge * separation distance
Electronegativity is based on the principle that the closer an electron is to the atomic nucleus, where postive charge is concentrated, the more attractive force the positive charge can exert on the electron.
As a result, as atomic radius decreases by one half, what happens to the force pulling the electron toward that atom?
Electronegativity is an important concept in physical chemistry, and often used to help quantify the dipole moment of polar compounds. Polar compounds are different from those compounds that are purely nonpolar or purely ionic. An example can be seen by contrasting sodium chloride, NaCl, with an organic molecule, R-C-OH. The former is purely ionic, and the latter is polar covalent.
When comparing more than one polar covalent molecule, we use the dipole moment value to help us determine relative strength of polarity. Dipole moment, however, is dependent on the electronegativity of the atoms making up the bond. Electronegativity is a property inherent to the atom in question, whereas dipole moment is a property of the bond between them.
For example, oxygen has an electronegativity of 3.44, and hydrogen of 2.20. In other words, oxygen more strongly attracts electrons when in a bond with hydrogen. This leads to the O-H bond having a dipole moment.
When all the dipole moments of polar bonds in a molecule are summed, the molecular dipole moment results, as per the following equation.
Dipole moment = charge * separation distance
Electronegativity is based on the principle that the closer an electron is to the atomic nucleus, where postive charge is concentrated, the more attractive force the positive charge can exert on the electron.
As a result, as atomic radius decreases by one half, what happens to the force pulling the electron toward that atom?
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This is a function of the equation 
.
In other words, as the distance between two charges doubles, the force between them goes increases, as the denominator decreases from 
to 
.
Here, we are decreasing the distance by 1/2, decreasing the denominator by 1/4, so our force goes up by 4 times.
This is a function of the equation
In other words, as the distance between two charges doubles, the force between them goes increases, as the denominator decreases from
Here, we are decreasing the distance by 1/2, decreasing the denominator by 1/4, so our force goes up by 4 times.
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Batteries and AC current are often used to charge a capacitor. A common example of capacitor use is in computer hard drives, where capacitors are charged in a specific pattern to code information. A simplified circuit with capacitors can be seen below. The capacitance of C1 is 0.5 μF and the capacitances of C2 and C3 are 1 μF each. A 10 V battery with an internal resistance of 1 Ω supplies the circuit.
Using the plate diagram above, what direction do the electric field lines point?
Batteries and AC current are often used to charge a capacitor. A common example of capacitor use is in computer hard drives, where capacitors are charged in a specific pattern to code information. A simplified circuit with capacitors can be seen below. The capacitance of C1 is 0.5 μF and the capacitances of C2 and C3 are 1 μF each. A 10 V battery with an internal resistance of 1 Ω supplies the circuit.
Using the plate diagram above, what direction do the electric field lines point?
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As with a point charge, remember that electric field lines point from areas of high potential to areas of low potential. Areas of high potential have positive (+) charge and areas of low potential have negative (-) charge, thus the electric field lines point to the right.
As with a point charge, remember that electric field lines point from areas of high potential to areas of low potential. Areas of high potential have positive (+) charge and areas of low potential have negative (-) charge, thus the electric field lines point to the right.
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For the following:
If a charge of magnitude +4e is being held in place 3 nm from a charge of -5e which is also being held in place. What is the potential energy of the system?
For the following:
If a charge of magnitude +4e is being held in place 3 nm from a charge of -5e which is also being held in place. What is the potential energy of the system?
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Given the equation and plugging in the values of e and k, we get that
It is important to keep in mind that the charge 
is given in the question and must be incorporated into the formula by multiplying each charge by that value.
Given the equation and plugging in the values of e and k, we get that
It is important to keep in mind that the charge
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If the electrical potential energy between two equal charges quadruples, describe the change in the distance between the particles.
If the electrical potential energy between two equal charges quadruples, describe the change in the distance between the particles.
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Electrical potential energy is given by the equation 
.
Electrical potential energy is inversely proportional to the distance between the two charges. If the energy is quadrupled, then 
(the distance between the two equal charges) must have decreased proportionally.
For the energy to be quadrupled, the radius must be quartered.
Electrical potential energy is given by the equation
Electrical potential energy is inversely proportional to the distance between the two charges. If the energy is quadrupled, then
For the energy to be quadrupled, the radius must be quartered.
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Which of the following is not true regarding electric potential?
Which of the following is not true regarding electric potential?
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A positive test charge will naturally move from high potential to low potential. If it is moved in the opposite direction, then the electric field will do work against its motion (negative work). This be seen from the equation for electric field work:
is the work done by the electric field, 
is the charge, and 
is the potential difference. If 
is positive (the final potential is higher than the initial potential) and 
is also positive, then work done by the field is negative.
A positive test charge will naturally move from high potential to low potential. If it is moved in the opposite direction, then the electric field will do work against its motion (negative work). This be seen from the equation for electric field work:
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How much work is required to bring together the three given charges from infinity to the corners of an equilateral triangle of side length 1cm?
How much work is required to bring together the three given charges from infinity to the corners of an equilateral triangle of side length 1cm?
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Relevant equations:
Step 1: Since the work done to assemble the charges equals their potential energy in this arrangment, find the potential energy between each pair of charges. Work is equal to change in potential energy; since the charges start at infinite distance, initially potential energy is equal to zero.
Charges 1 and 2
Charges 1 and 3
Charges 2 and 3
Step 2: Add together all these potential energies to find the total energy of the arrangement.
Relevant equations:
Step 1: Since the work done to assemble the charges equals their potential energy in this arrangment, find the potential energy between each pair of charges. Work is equal to change in potential energy; since the charges start at infinite distance, initially potential energy is equal to zero.
Charges 1 and 2
Charges 1 and 3
Charges 2 and 3
Step 2: Add together all these potential energies to find the total energy of the arrangement.
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A standard AC outlet is capable of delivering 
of current. What is the maximum possible voltage given by the outlet.
A standard AC outlet is capable of delivering
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Since the given voltage is the root mean squared voltage we must multiply the voltage by 
to find the maximum voltage.
We determine that the maximum voltage delivered by the outlet is 
.
Since the given voltage is the root mean squared voltage we must multiply the voltage by
We determine that the maximum voltage delivered by the outlet is
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A neutral conducting sphere rests on an insulating styrofoam block. A student then places his hand on the sphere, maintaining this contact as a negatively charged plastic rod is brought near the sphere without touching. While the plastic rod is still nearby, the student removes his hand. Finally, the rod is also removed. Which of the following best describes the final charge on the sphere?
A neutral conducting sphere rests on an insulating styrofoam block. A student then places his hand on the sphere, maintaining this contact as a negatively charged plastic rod is brought near the sphere without touching. While the plastic rod is still nearby, the student removes his hand. Finally, the rod is also removed. Which of the following best describes the final charge on the sphere?
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The student's hand on the sphere "grounds" it, allowing charges to flow in or out. No charge flows through the styrofoam insulator. When the negatively charged rod is brought nearby, negative charges in the sphere are repelled and exit via the student's hand, giving the sphere a net positive charge. After the student removes his hand, no more charges can flow into or out from the sphere, so the net positive charge remains after the rod is removed. Since this is a conducting sphere, the charges will spread out evenly over the surface.
The student's hand on the sphere "grounds" it, allowing charges to flow in or out. No charge flows through the styrofoam insulator. When the negatively charged rod is brought nearby, negative charges in the sphere are repelled and exit via the student's hand, giving the sphere a net positive charge. After the student removes his hand, no more charges can flow into or out from the sphere, so the net positive charge remains after the rod is removed. Since this is a conducting sphere, the charges will spread out evenly over the surface.
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How much energy is required by a 
lightbulb running for 
minutes?
How much energy is required by a
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Power is given in watts which is equal to 
Convert 10 minutes into seconds and then multiply the time in seconds with the number of watts to obtain the joules of energy required by the lightbulb.
Power is given in watts which is equal to
Convert 10 minutes into seconds and then multiply the time in seconds with the number of watts to obtain the joules of energy required by the lightbulb.
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The primary coil of a transformer has 800 turns and an rms voltage of 400V. If an output voltage of 120V is needed, how many turns whould the secondary coil contain?
The primary coil of a transformer has 800 turns and an rms voltage of 400V. If an output voltage of 120V is needed, how many turns whould the secondary coil contain?
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Relevant equations:
For the primary coil, we have:
And for the secondary coil:
Plugging these in yields:
Relevant equations:
For the primary coil, we have:
And for the secondary coil:
Plugging these in yields:
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An electrical current is flowing through a block. It is observed that the electrical conductivity of the block is 
, the length of the block is 
and the resistance of the block is 
. Which of the following is a valid conclusion about this block?
An electrical current is flowing through a block. It is observed that the electrical conductivity of the block is
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To answer this question you need to understand the relationship between electrical conductivity, 
, and electrical resistivity, 
:
This means that the electrical conductivity is the reciprocal of the electrical resistivity; therefore, the electrical resistivity of this block is:
Recall the definition of resistivity:
Here, 
is the resistance, 
is the cross-sectional area, and 
is the length of the block. The question gives us resistance and length of the block, and we calculated resistivity; therefore, solving for the area of the block gives us:
The cross-sectional area of the block is 
.
Of the given answer choices, the only valid conclusion is that the block has a square cross-section with a height and width of 
because this square has an area equal to the cross-sectional area of the block (
).
To answer this question you need to understand the relationship between electrical conductivity,
This means that the electrical conductivity is the reciprocal of the electrical resistivity; therefore, the electrical resistivity of this block is:
Recall the definition of resistivity:
Here,
The cross-sectional area of the block is
Of the given answer choices, the only valid conclusion is that the block has a square cross-section with a height and width of
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Consider a conducting rod. Which of the following is true regarding the relationship between the electrical conductivity, the resistance, and the length of the rod?
Consider a conducting rod. Which of the following is true regarding the relationship between the electrical conductivity, the resistance, and the length of the rod?
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The electrical conductivity is the reciprocal of electrical resistivity; therefore, an increase in electrical resistivity will lead to a decrease in electrical conductivity, and vice versa.
Recall the definition of electrical resistivity:
Here, 
is resistance, 
is cross-sectional area, and 
is the length of the rod. This equation reveals that an increase in resistance and area will increase resistivity, whereas an increase in length will decrease resistivity. Since conductivity is the reciprocal of resistivity, increasing resistance and area will decrease conductivity, whereas increasing the length will increase conductivity.
The electrical conductivity is the reciprocal of electrical resistivity; therefore, an increase in electrical resistivity will lead to a decrease in electrical conductivity, and vice versa.
Recall the definition of electrical resistivity:
Here,
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A researcher has two rods: rod A and rod B. Rod A has the same geometrical properties as rod B, but has a larger resistance. What can you conclude about the relative rates of charge flow in the two rods?
A researcher has two rods: rod A and rod B. Rod A has the same geometrical properties as rod B, but has a larger resistance. What can you conclude about the relative rates of charge flow in the two rods?
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The question is asking about the rates of charge flow. Recall that the current is defined as the amount of charge flowing through a point in a given time; therefore, we are looking for the amount of current flowing through the two rods. Current flow is higher for a material with higher electrical conductivity. This means that we need to find the rod with the higher electrical conductivity.
Since there are no easy equations to find conductivity, we need to find the resistivity first. Electrical conductivity is the reciprocal of electrical resistivity (measure of the ability of a material to resist current flow); therefore, an increase in resistivity leads to a decrease in conductivity, and vice versa. Resistivity is defined as:
Here, 
is the resistance, 
is the cross-sectional area, and 
is the length of the rod. The question states that the two rods have the same geometrical properties; therefore, the area and the length of the rods are the same. However, the resistance of rod A is higher. This means that the resistivity is higher and conductivity, consequently, is lower for rod A. Since it has a lower conductivity, rod A has a lower charge flow rate.
The question is asking about the rates of charge flow. Recall that the current is defined as the amount of charge flowing through a point in a given time; therefore, we are looking for the amount of current flowing through the two rods. Current flow is higher for a material with higher electrical conductivity. This means that we need to find the rod with the higher electrical conductivity.
Since there are no easy equations to find conductivity, we need to find the resistivity first. Electrical conductivity is the reciprocal of electrical resistivity (measure of the ability of a material to resist current flow); therefore, an increase in resistivity leads to a decrease in conductivity, and vice versa. Resistivity is defined as:
Here,
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Which of the following is false regarding a battery?
Which of the following is false regarding a battery?
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Batteries are a series of electrochemical cells that use the electrical energy associated with the movement of electrons to perform other processes. The electrical energy is not itself usable; instead, batteries convert the electrical energy into other forms of energy, such as chemical energy, that can be used to drive a process. The electrical energy is derived from the movement of electrons associated with redox reactions.
Batteries contain one or more electrochemical cells. Each electrochemical cell houses a cathode and an anode, which facilitate a redox reaction. The cathode is the site of the reduction half-reaction, whereas the anode is the site of the oxidation half-reaction. Reduction is the process by which reactants gain electrons and become more negative; oxidation is the process by which reactants lose electrons and become more positive. As such, electrons are products at an anode and reactants at a cathode. The redox reaction proceeds in the spontaneous reaction direction when the battery is being used, but proceeds in the nonspontaneous reaction direction when the battery is being recharged after use. Recall that nonspontaneous reactions require energy. When you are charging a battery, you are supplying energy in the form of voltage to drive the nonspontaneous reaction. On the other hand, when you are discharging (or using) the battery, the spontaneous redox reaction is supplying energy to drive another process.
Batteries are a series of electrochemical cells that use the electrical energy associated with the movement of electrons to perform other processes. The electrical energy is not itself usable; instead, batteries convert the electrical energy into other forms of energy, such as chemical energy, that can be used to drive a process. The electrical energy is derived from the movement of electrons associated with redox reactions.
Batteries contain one or more electrochemical cells. Each electrochemical cell houses a cathode and an anode, which facilitate a redox reaction. The cathode is the site of the reduction half-reaction, whereas the anode is the site of the oxidation half-reaction. Reduction is the process by which reactants gain electrons and become more negative; oxidation is the process by which reactants lose electrons and become more positive. As such, electrons are products at an anode and reactants at a cathode. The redox reaction proceeds in the spontaneous reaction direction when the battery is being used, but proceeds in the nonspontaneous reaction direction when the battery is being recharged after use. Recall that nonspontaneous reactions require energy. When you are charging a battery, you are supplying energy in the form of voltage to drive the nonspontaneous reaction. On the other hand, when you are discharging (or using) the battery, the spontaneous redox reaction is supplying energy to drive another process.
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In a battery, the is the site of the reduction half-reaction and the is the electrode where the oxidation number of the reactant increases.
In a battery, the is the site of the reduction half-reaction and the is the electrode where the oxidation number of the reactant increases.
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An electrochemical cell in a battery contains two electrodes: the anode and the cathode. Anodes are the site of oxidation half-reactions and cathodes are the site of reduction half-reactions. Recall that oxidation involves loss of electrons from reactants. The reactants at the anode become more positive, and there is an increase in their oxidation number. Reduction, on the other hand, involves a gain of electrons and a decrease in the reactant oxidation number at the cathode.
An electrochemical cell in a battery contains two electrodes: the anode and the cathode. Anodes are the site of oxidation half-reactions and cathodes are the site of reduction half-reactions. Recall that oxidation involves loss of electrons from reactants. The reactants at the anode become more positive, and there is an increase in their oxidation number. Reduction, on the other hand, involves a gain of electrons and a decrease in the reactant oxidation number at the cathode.
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Two charges of 
coulombs are a distance 
apart from each other. Which of the following would reduce the force exerted between the charges by a factor of 4?
Two charges of
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Given Coulomb's Law electrostatic forces: 
We can see that distance and force are inversly related. Also distance is squared, so if we increase the distance by 2, the force between the two charges will be reduced by a factor of four.
Given Coulomb's Law electrostatic forces:
We can see that distance and force are inversly related. Also distance is squared, so if we increase the distance by 2, the force between the two charges will be reduced by a factor of four.
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How many electrons would it require to generate a 5 N attractive force on a +3 µC charge from 0.1 m away.
How many electrons would it require to generate a 5 N attractive force on a +3 µC charge from 0.1 m away.
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To find the answer we must first solve for q, using Coulomb's Law. Then after finding q = 1.85 x 10–6 C, we must divide by 1.6 x 10–19 C to get the amount of electrons required to make such a charge.
To find the answer we must first solve for q, using Coulomb's Law. Then after finding q = 1.85 x 10–6 C, we must divide by 1.6 x 10–19 C to get the amount of electrons required to make such a charge.
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Two charges Q1 and Q2 are held stationary 1 m away from each other. The magnitude of charge of Q2 is twice that of Q1. A positive point charge A is placed directly in the middle of the two charges (Q1 and Q2). What is the ratio of the net force on charge A when Q1 and Q2 are both negative over the net force on charge A when Q1 is negative and Q2 is positive?
Two charges Q1 and Q2 are held stationary 1 m away from each other. The magnitude of charge of Q2 is twice that of Q1. A positive point charge A is placed directly in the middle of the two charges (Q1 and Q2). What is the ratio of the net force on charge A when Q1 and Q2 are both negative over the net force on charge A when Q1 is negative and Q2 is positive?
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For this problem we must understand Coulomb's Law. The force on charge A will be dircetly affected by the charge of Q1 and Q2. Q1 and Q2 are both negative, they will both attract charge A, and the net force will be reduced as they pull in opposite directions. Switching Q2 to a positive charge will result in a repulsive force on charge A which will be in the same direction as the attractive force between Q1 and A.
For this problem we must understand Coulomb's Law. The force on charge A will be dircetly affected by the charge of Q1 and Q2. Q1 and Q2 are both negative, they will both attract charge A, and the net force will be reduced as they pull in opposite directions. Switching Q2 to a positive charge will result in a repulsive force on charge A which will be in the same direction as the attractive force between Q1 and A.
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