Q: A parallel-plate capacitor has plates of area $$A = 1.0 \times 10$$^{-4}$$ \ \mathrm{m}^2$$ separated by $$2.0 \ \mathrm{cm}$$ and charged to $$+5.0 \ \mathrm{nC}$$ and $$-5.0 \ \mathrm{nC}. If a $$surface of area $$A is $$tilted at $$45^\circ to $$the field, what is the electric flux through the surface? (Assume $$E = 5.65 \times 10^4$ \ \mathrm{N/C})$$

$$\Phi_E = (5.65 \times 10^4$) \times (1.0 \times 10$$^{-4}$$) \times \cos 45^\circ = 4.0 \ \mathrm{Nm}^2/\mathrm{C}$$

Question 1

Which of the following statements best describes the electric field outside a uniformly charged sphere of radius $$R$$ and total charge $$Q$$?

Accepted Answer

It is the same as the field produced by a point charge $$Q$$ located at the center of the sphere.

Question 2

A parallel-plate capacitor has plates of area $$A = 1.0 	imes 10$$^{-4}$$ \ \mathrm{m}^2$$ separated by $$2.0 \ \mathrm{cm}$$ and charged to $$+5.0 \ \mathrm{nC}$$ and $$-5.0 \ \mathrm{nC}. If a $$surface of area $$A is $$tilted at $$45^\circ to $$the field, what is the electric flux through the surface? (Assume $$E = 5.65 	imes 10^4$ \ \mathrm{N/C})$$

Accepted Answer

$$\Phi_E = (5.65 	imes 10^4$) 	imes (1.0 	imes 10$$^{-4}$$) 	imes \cos 45^\circ = 4.0 \ \mathrm{Nm}^2/\mathrm{C}$$

Question 3

Which symmetry is most appropriate for applying Gauss’s law to an infinitely long charged cylinder?

Accepted Answer

Cylindrical symmetry

Question 4

A Gaussian surface encloses a point charge $$q. $$What is the electric flux through the surface?

Accepted Answer

$$\Phi_E = q/\$$epsilon_0$$

Question 5

If a closed Gaussian surface contains no net charge, which of the following is true?

Accepted Answer

The electric flux through the surface is zero.

Question 6

A nonuniform electric field passes through a curved surface. How is the total electric flux through the surface calculated?

Accepted Answer

By integrating $$\vec{E} \cdot d\vec{A}$$ over the entire surface: $$\Phi_E = \int \vec{E} \cdot d\vec{A}$$

Question 7

What is the direction of the area vector $$\vec{A}$$ for a flat surface?

Accepted Answer

Perpendicular to the surface

Question 8

A conductor is in electrostatic equilibrium. What is the electric field inside the conductor?

Accepted Answer

It is zero everywhere inside the conductor.

Question 9

The electric field just outside the surface of a charged conductor is:

Accepted Answer

$$E = \sigma/\$$epsilon_0$$, perpendicular to the surface

Question 10

A Faraday cage is used to shield a region from external electric fields. What physical principle explains why the field inside the cage is zero?

Accepted Answer

The charges on the cage rearrange so that the net electric field inside is zero.

Question 11

An infinite plane of charge has surface charge density $$\sigma. $$What is the magnitude of the electric field just outside the plane?

Accepted Answer

$$E = \sigma/2\$$epsilon_0$$

Question 12

A spherical Gaussian surface of radius $$r$$ encloses a total charge $$Q. $$What is the electric field at the surface?

Accepted Answer

$$E = Q/(4\pi\$$epsilon_0$$ r^2$)$$

Question 13

A charged conductor has a hollow cavity inside. If there is no charge inside the cavity, what is the electric field inside the cavity?

Accepted Answer

Zero everywhere inside the cavity.

Question 14

A $$2.0 cm $$diameter brass sphere is given a charge of $$2.0 	imes 10$$^{-7}$$ C. What is the electric field strength at its surface?

Accepted Answer

$$E = \dfrac{Q}{4\pi\$$epsilon_0$$ R^2$}$$

Question 15

Which of the following is NOT a fundamental symmetry used in applying Gauss’s law?

Accepted Answer

Elliptical symmetry

Question 16

A closed Gaussian surface encloses multiple point charges. What is the total electric flux through the surface?

Accepted Answer

$$\Phi_E = Q_{	ext{in}}/\$$epsilon_0$$, where Q$$_{	ext{in}}$$ is the sum of all enclosed charges

Question 17

If the electric field is everywhere tangent to a closed surface, what is the electric flux through the surface?

Accepted Answer

Zero

Question 18

Which of the following is a correct application of Gauss’s law?

Accepted Answer

It can be used to find the electric field only when the symmetry of the charge distribution matches the symmetry of the Gaussian surface.

Gauss's Law and Symmetry in Electrostatics

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