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AP Physics C Electricity : Understanding Electrostatics

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Example Questions

Example Question #1 : Electricity And Magnetism Exam

A hollow metal sphere with a diameter of 10cm has a net charge of $4\mu C$ distributed uniformly across its surface. What is the magnitude of the field a distance 2.0m from the center of the sphere?

$k = 9.0 * 10^9 \frac{N\cdot m^2}{C^2}$

Possible Answers:

$3.6 * 10^4 \frac{N}{C}$

$9.0 * 10^3 \frac{N}{C}$

$8.6*10^3 \frac{N}{C}$

$1.8 * 10^4 \frac{N}{C}$

$2.7 * 10^{4} \frac{N}{C}$

Correct answer:

$8.6*10^3 \frac{N}{C}$

Explanation:

Relevant equations:

$E = \frac{kq}{r^2}$ (electric field of point charge)

Anywhere outside the metal sphere, the electric field is the same as it would be for a point charge of the same magnitude, located at the center of the sphere. So, calculate the electric field of a point charge given:

$q = 4.0 * 10^{-6}C$

r = 2.0m+0.05m=2.05m

$k = 9.0 * 10^9 \frac{N\cdot m^2}{C^2}$

Plugging in gives:

$E = \frac{(9.0*10^9\frac{N\cdot m^2}{C^2})(4.0 * 10^{-6}C)}{(2.05m)^2}=\frac{36000}{4.2} \frac{N}{C}=8.6*10^3 \frac{N}{C}$

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Example Question #1 : Electricity And Magnetism Exam

Two infinite parallel conducting sheets each have positive charge density $\sigma$ . What is the magnitude and direction of the electric field to the right of the right sheet?

Possible Answers:

$\frac{\sigma}{2 \epsilon _o}$ , to the right

$\frac{2 \sigma}{\epsilon _o}$ , to the left

$\frac{\sigma}{\epsilon _o}$ , to the right

$\frac{2 \sigma}{\epsilon _o}$ , to the right

Correct answer:

$\frac{\sigma}{\epsilon _o}$ , to the right

Explanation:

Relevant equations:

$E = \frac{\sigma }{2 \epsilon _o}$ (field due to single infinite plane)

Electric field is additive; in other words, the total electric field from the two planes is the sum of their individual fields:

$E_{total} = E_1 + E_2$

$E _{total} = \frac{\sigma}{2 \epsilon _o}+\frac{\sigma}{2 \epsilon _o}$

$E_{total}=\frac{\sigma}{\epsilon_o}$

The direction of the electric field is away from positive source charges. Thus, to the right of these positively charged planes, the field points away to the right.

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Example Question #3 : Electricity And Magnetism Exam

Consider a spherical capacitor made of two nested spheres. The smaller sphere has a radius of R_1 and a charge of , and lies within a larger sphere with radius R_2 and a charge of .

Which of the following equations accurately describes the capacitance of this spherical capacitor?

Possible Answers:

$C = \frac{R_{1}R_{2}}{k(R_{2} - R_{1})}$

$C = \frac{(R_{2} - R_{1})}{R_{1}R_{2}}$

$C = \frac{R_{2}}{k(R_{2} - R_{1})}{}$

$C = \frac{R_{1}}{k(R_{2} - R_{1})}{}$

Due to symmetry, this scenario would not produce capacitance

Correct answer:

$C = \frac{R_{1}R_{2}}{k(R_{2} - R_{1})}$

Explanation:

To solve this problem, we will need to derive an equation.

We know that:

$C=\left | \frac{Q}{V}\right |$

$V=\oint E\cdot dr$

We can use Gauss's law to derive the electric field between the two circles yielding:

$E = \frac{Q}{\epsilon_{0}4\pi r^2}$

Doing our integration with respect to from R_1 to R_2 , we get:

$V = \frac{-Q(R_{2} - R_{1})}{\epsilon _{0}4\pi R_{1}R_{2}}$

We can plug this back into our equation for capacitance to get:

$C = \frac{R_{1}R_{2}}{k(R_{2} - R_{1})}$

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All AP Physics C Electricity Resources

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AP Physics C Electricity : Understanding Electrostatics

Study concepts, example questions & explanations for AP Physics C Electricity

All AP Physics C Electricity Resources

Example Questions

Example Question #1 : Electricity And Magnetism Exam

Example Question #1 : Electricity And Magnetism Exam

Example Question #3 : Electricity And Magnetism Exam

All AP Physics C Electricity Resources

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