Electric Potential Energy - MCAT Physical

Card 0 of 35

Question

For the following:

$e = 1.60 \times 10^{-19}$

$k = 8.99 \times 10^{9}$

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?

Answer

$U= \frac{kQq}{r}$

Given the equation and plugging in the values of e and k, we get that

$U= 1.53\times 10^{-18}$

It is important to keep in mind that the charge $e$ is given in the question and must be incorporated into the formula by multiplying each charge by that value.

Compare your answer with the correct one above

Question

If the electrical potential energy between two equal charges quadruples, describe the change in the distance between the particles.

Answer

Electrical potential energy is given by the equation $U=\frac{kq_1q_2}{r}$ .

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.

$U=\frac{kq_1q_2}{r}$

$4U=\frac{kq_1q_2}{x(r)}$

$4U=\frac{kq_1q_2}{(\frac{1}{4})r}=4\frac{kq_1q_2}{r}$

For the energy to be quadrupled, the radius must be quartered.

Compare your answer with the correct one above

Question

Which of the following is not true regarding electric potential?

Answer

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:

$W=-q\Delta V$

$\small W$ is the work done by the electric field, $\small q$ is the charge, and $\small \Delta V$ is the potential difference. If $\small \Delta V$ is positive (the final potential is higher than the initial potential) and $\small q$ is also positive, then work done by the field is negative.

Compare your answer with the correct one above

Question

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?

$q_1 = 1\mu C,\ q_2=2\mu C,\ q_3=3\mu C$

Answer

Relevant equations:

$U = \frac{kq_1q_2}{r}$

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

$U_{12} = \frac{kq_1q_2}{r_{12}}= \frac{(910^9)(110^{-6})(210^{-6})}{0.01}=1.8 J$

Charges 1 and 3*

$U_{13}=\frac{kq_1q_3}{r_{13}}=\frac{(910^9)(110^{-6})(310^{-6})}{0.01}=2.7J$

Charges 2 and 3*

$U_{23} = \frac{kq_2q_3}{r_{23}}=\frac{(910^9)(210^{-6})(3*10^{-6})}{0.01}=5.4J$

Step 2: Add together all these potential energies to find the total energy of the arrangement.

$U = U_{12}+U_{13}+U_{23}= 1.8+2.7+5.4 = 9.9J$

Compare your answer with the correct one above

Question

A standard AC outlet is capable of delivering $120V_{rms}$ of current. What is the maximum possible voltage given by the outlet.

Answer

Since the given voltage is the root mean squared voltage we must multiply the voltage by $\sqrt{2}$ to find the maximum voltage.

$120V \cdot\sqrt{2} = 120V \cdot 1.4= 170V$

We determine that the maximum voltage delivered by the outlet is .

Compare your answer with the correct one above

Question

For the following:

$e = 1.60 \times 10^{-19}$

$k = 8.99 \times 10^{9}$

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?

Answer

$U= \frac{kQq}{r}$

Given the equation and plugging in the values of e and k, we get that

$U= 1.53\times 10^{-18}$

It is important to keep in mind that the charge $e$ is given in the question and must be incorporated into the formula by multiplying each charge by that value.

Compare your answer with the correct one above

Question

If the electrical potential energy between two equal charges quadruples, describe the change in the distance between the particles.

Answer

Electrical potential energy is given by the equation $U=\frac{kq_1q_2}{r}$ .

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.

$U=\frac{kq_1q_2}{r}$

$4U=\frac{kq_1q_2}{x(r)}$

$4U=\frac{kq_1q_2}{(\frac{1}{4})r}=4\frac{kq_1q_2}{r}$

For the energy to be quadrupled, the radius must be quartered.

Compare your answer with the correct one above

Question

Which of the following is not true regarding electric potential?

Answer

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:

$W=-q\Delta V$

$\small W$ is the work done by the electric field, $\small q$ is the charge, and $\small \Delta V$ is the potential difference. If $\small \Delta V$ is positive (the final potential is higher than the initial potential) and $\small q$ is also positive, then work done by the field is negative.

Compare your answer with the correct one above

Question

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?

$q_1 = 1\mu C,\ q_2=2\mu C,\ q_3=3\mu C$

Answer

Relevant equations:

$U = \frac{kq_1q_2}{r}$

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

$U_{12} = \frac{kq_1q_2}{r_{12}}= \frac{(910^9)(110^{-6})(210^{-6})}{0.01}=1.8 J$

Charges 1 and 3*

$U_{13}=\frac{kq_1q_3}{r_{13}}=\frac{(910^9)(110^{-6})(310^{-6})}{0.01}=2.7J$

Charges 2 and 3*

$U_{23} = \frac{kq_2q_3}{r_{23}}=\frac{(910^9)(210^{-6})(3*10^{-6})}{0.01}=5.4J$

Step 2: Add together all these potential energies to find the total energy of the arrangement.

$U = U_{12}+U_{13}+U_{23}= 1.8+2.7+5.4 = 9.9J$

Compare your answer with the correct one above

Question

A standard AC outlet is capable of delivering $120V_{rms}$ of current. What is the maximum possible voltage given by the outlet.

Answer

Since the given voltage is the root mean squared voltage we must multiply the voltage by $\sqrt{2}$ to find the maximum voltage.

$120V \cdot\sqrt{2} = 120V \cdot 1.4= 170V$

We determine that the maximum voltage delivered by the outlet is .

Compare your answer with the correct one above

Question

For the following:

$e = 1.60 \times 10^{-19}$

$k = 8.99 \times 10^{9}$

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?

Answer

$U= \frac{kQq}{r}$

Given the equation and plugging in the values of e and k, we get that

$U= 1.53\times 10^{-18}$

It is important to keep in mind that the charge $e$ is given in the question and must be incorporated into the formula by multiplying each charge by that value.

Compare your answer with the correct one above

Question

If the electrical potential energy between two equal charges quadruples, describe the change in the distance between the particles.

Answer

Electrical potential energy is given by the equation $U=\frac{kq_1q_2}{r}$ .

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.

$U=\frac{kq_1q_2}{r}$

$4U=\frac{kq_1q_2}{x(r)}$

$4U=\frac{kq_1q_2}{(\frac{1}{4})r}=4\frac{kq_1q_2}{r}$

For the energy to be quadrupled, the radius must be quartered.

Compare your answer with the correct one above

Question

Which of the following is not true regarding electric potential?

Answer

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:

$W=-q\Delta V$

$\small W$ is the work done by the electric field, $\small q$ is the charge, and $\small \Delta V$ is the potential difference. If $\small \Delta V$ is positive (the final potential is higher than the initial potential) and $\small q$ is also positive, then work done by the field is negative.

Compare your answer with the correct one above

Question

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?

$q_1 = 1\mu C,\ q_2=2\mu C,\ q_3=3\mu C$

Answer

Relevant equations:

$U = \frac{kq_1q_2}{r}$

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

$U_{12} = \frac{kq_1q_2}{r_{12}}= \frac{(910^9)(110^{-6})(210^{-6})}{0.01}=1.8 J$

Charges 1 and 3*

$U_{13}=\frac{kq_1q_3}{r_{13}}=\frac{(910^9)(110^{-6})(310^{-6})}{0.01}=2.7J$

Charges 2 and 3*

$U_{23} = \frac{kq_2q_3}{r_{23}}=\frac{(910^9)(210^{-6})(3*10^{-6})}{0.01}=5.4J$

Step 2: Add together all these potential energies to find the total energy of the arrangement.

$U = U_{12}+U_{13}+U_{23}= 1.8+2.7+5.4 = 9.9J$

Compare your answer with the correct one above

Question

A standard AC outlet is capable of delivering $120V_{rms}$ of current. What is the maximum possible voltage given by the outlet.

Answer

Since the given voltage is the root mean squared voltage we must multiply the voltage by $\sqrt{2}$ to find the maximum voltage.

$120V \cdot\sqrt{2} = 120V \cdot 1.4= 170V$

We determine that the maximum voltage delivered by the outlet is .

Compare your answer with the correct one above

Question

For the following:

$e = 1.60 \times 10^{-19}$

$k = 8.99 \times 10^{9}$

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?

Answer

$U= \frac{kQq}{r}$

Given the equation and plugging in the values of e and k, we get that

$U= 1.53\times 10^{-18}$

It is important to keep in mind that the charge $e$ is given in the question and must be incorporated into the formula by multiplying each charge by that value.

Compare your answer with the correct one above

Question

If the electrical potential energy between two equal charges quadruples, describe the change in the distance between the particles.

Answer

Electrical potential energy is given by the equation $U=\frac{kq_1q_2}{r}$ .

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.

$U=\frac{kq_1q_2}{r}$

$4U=\frac{kq_1q_2}{x(r)}$

$4U=\frac{kq_1q_2}{(\frac{1}{4})r}=4\frac{kq_1q_2}{r}$

For the energy to be quadrupled, the radius must be quartered.

Compare your answer with the correct one above

Question

Which of the following is not true regarding electric potential?

Answer

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:

$W=-q\Delta V$

$\small W$ is the work done by the electric field, $\small q$ is the charge, and $\small \Delta V$ is the potential difference. If $\small \Delta V$ is positive (the final potential is higher than the initial potential) and $\small q$ is also positive, then work done by the field is negative.

Compare your answer with the correct one above

Question

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?

$q_1 = 1\mu C,\ q_2=2\mu C,\ q_3=3\mu C$

Answer

Relevant equations:

$U = \frac{kq_1q_2}{r}$

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

$U_{12} = \frac{kq_1q_2}{r_{12}}= \frac{(910^9)(110^{-6})(210^{-6})}{0.01}=1.8 J$

Charges 1 and 3*

$U_{13}=\frac{kq_1q_3}{r_{13}}=\frac{(910^9)(110^{-6})(310^{-6})}{0.01}=2.7J$

Charges 2 and 3*

$U_{23} = \frac{kq_2q_3}{r_{23}}=\frac{(910^9)(210^{-6})(3*10^{-6})}{0.01}=5.4J$

Step 2: Add together all these potential energies to find the total energy of the arrangement.

$U = U_{12}+U_{13}+U_{23}= 1.8+2.7+5.4 = 9.9J$

Compare your answer with the correct one above

Question

A standard AC outlet is capable of delivering $120V_{rms}$ of current. What is the maximum possible voltage given by the outlet.

Answer

Since the given voltage is the root mean squared voltage we must multiply the voltage by $\sqrt{2}$ to find the maximum voltage.

$120V \cdot\sqrt{2} = 120V \cdot 1.4= 170V$

We determine that the maximum voltage delivered by the outlet is .

Compare your answer with the correct one above

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Electric Potential Energy - MCAT Physical

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?

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.

If the electrical potential energy between two equal charges quadruples, describe the change in the distance between the particles.

Which of the following is not true regarding electric potential?

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?

A standard AC outlet is capable of delivering of current. What is the maximum possible voltage given by the outlet.

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 .

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?

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.

If the electrical potential energy between two equal charges quadruples, describe the change in the distance between the particles.

Which of the following is not true regarding electric potential?

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?

A standard AC outlet is capable of delivering of current. What is the maximum possible voltage given by the outlet.

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 .

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?

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.

If the electrical potential energy between two equal charges quadruples, describe the change in the distance between the particles.

Which of the following is not true regarding electric potential?

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?

A standard AC outlet is capable of delivering of current. What is the maximum possible voltage given by the outlet.

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 .

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?

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.

If the electrical potential energy between two equal charges quadruples, describe the change in the distance between the particles.

Which of the following is not true regarding electric potential?

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?

A standard AC outlet is capable of delivering of current. What is the maximum possible voltage given by the outlet.

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 .

For the following:

$e = 1.60 \times 10^{-19}$

$k = 8.99 \times 10^{9}$

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?

$U= \frac{kQq}{r}$

Given the equation and plugging in the values of e and k, we get that

$U= 1.53\times 10^{-18}$

It is important to keep in mind that the charge $e$ is given in the question and must be incorporated into the formula by multiplying each charge by that value.

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?

$q_1 = 1\mu C,\ q_2=2\mu C,\ q_3=3\mu C$

A standard AC outlet is capable of delivering $120V_{rms}$ of current. What is the maximum possible voltage given by the outlet.

Since the given voltage is the root mean squared voltage we must multiply the voltage by $\sqrt{2}$ to find the maximum voltage.

$120V \cdot\sqrt{2} = 120V \cdot 1.4= 170V$

We determine that the maximum voltage delivered by the outlet is .

For the following:

$e = 1.60 \times 10^{-19}$

$k = 8.99 \times 10^{9}$

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?

$U= \frac{kQq}{r}$

Given the equation and plugging in the values of e and k, we get that

$U= 1.53\times 10^{-18}$

It is important to keep in mind that the charge $e$ is given in the question and must be incorporated into the formula by multiplying each charge by that value.

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?

$q_1 = 1\mu C,\ q_2=2\mu C,\ q_3=3\mu C$

A standard AC outlet is capable of delivering $120V_{rms}$ of current. What is the maximum possible voltage given by the outlet.

Since the given voltage is the root mean squared voltage we must multiply the voltage by $\sqrt{2}$ to find the maximum voltage.

$120V \cdot\sqrt{2} = 120V \cdot 1.4= 170V$

We determine that the maximum voltage delivered by the outlet is .

For the following:

$e = 1.60 \times 10^{-19}$

$k = 8.99 \times 10^{9}$

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?

$U= \frac{kQq}{r}$

Given the equation and plugging in the values of e and k, we get that

$U= 1.53\times 10^{-18}$

It is important to keep in mind that the charge $e$ is given in the question and must be incorporated into the formula by multiplying each charge by that value.

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?

$q_1 = 1\mu C,\ q_2=2\mu C,\ q_3=3\mu C$

A standard AC outlet is capable of delivering $120V_{rms}$ of current. What is the maximum possible voltage given by the outlet.

Since the given voltage is the root mean squared voltage we must multiply the voltage by $\sqrt{2}$ to find the maximum voltage.

$120V \cdot\sqrt{2} = 120V \cdot 1.4= 170V$

We determine that the maximum voltage delivered by the outlet is .

For the following:

$e = 1.60 \times 10^{-19}$

$k = 8.99 \times 10^{9}$

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?

$U= \frac{kQq}{r}$

Given the equation and plugging in the values of e and k, we get that

$U= 1.53\times 10^{-18}$

It is important to keep in mind that the charge $e$ is given in the question and must be incorporated into the formula by multiplying each charge by that value.

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?

$q_1 = 1\mu C,\ q_2=2\mu C,\ q_3=3\mu C$

A standard AC outlet is capable of delivering $120V_{rms}$ of current. What is the maximum possible voltage given by the outlet.

Since the given voltage is the root mean squared voltage we must multiply the voltage by $\sqrt{2}$ to find the maximum voltage.

$120V \cdot\sqrt{2} = 120V \cdot 1.4= 170V$

We determine that the maximum voltage delivered by the outlet is .