Q: Which of the following best describes the electric flux $$\Phi_E$$ through a flat surface of area $$A$$ placed in a uniform electric field $$\vec{E}$$, where the surface is tilted at an angle $$\theta$$ with respect to the field direction?

$$\Phi_E = E \cdot A \cdot \cos \theta$$

Q: A disk of radius $$0.10\,\mathrm{m} is $$placed in a uniform electric field of $$2 \times 10^3$\,\mathrm{N/C} at an $$angle of $$30^\circ to $$the field. What is the electric flux through the disk?

$$\Phi_E = 2 \times 10^3$ \times \pi \times (0.10)^2$ \times \cos 30^\circ$$

Q: A solid metal sphere of radius $$0.450\,\mathrm{m}$$ carries a net charge of $$0.250\,\mathrm{nC}. $$What is the magnitude of the electric field at a point $$0.100\,\mathrm{m}$$ outside the surface?

$$E = \dfrac{1}{4 \pi \$$epsilon_0$$} \dfrac{0.250 \times 10$$^{-9}$$}{(0.550)^2$}$$

Question 1

Which of the following best describes the electric flux $$\Phi_E$$ through a flat surface of area $$A$$ placed in a uniform electric field $$\vec{E}$$, where the surface is tilted at an angle $$	heta$$ with respect to the field direction?

Accepted Answer

$$\Phi_E = E \cdot A \cdot \cos 	heta$$

Question 2

A cube of side $$L is $$placed in a uniform electric field $$\vec{E}$$ such that the field is parallel to one of its faces. What is the net electric flux through the cube?

Accepted Answer

$$\Phi_E = 0$$

Question 3

A point charge $$q is $$placed at the center of a spherical Gaussian surface of radius $$r. $$What is the electric flux through the surface?

Accepted Answer

$$\Phi_E = \dfrac{q}{\$$epsilon_0$$}$$

Question 4

A disk of radius $$0.10\,\mathrm{m} is $$placed in a uniform electric field of $$2 	imes 10^3$\,\mathrm{N/C} at an $$angle of $$30^\circ to $$the field. What is the electric flux through the disk?

Accepted Answer

$$\Phi_E = 2 	imes 10^3$ 	imes \pi 	imes (0.10)^2$ 	imes \cos 30^\circ$$

Question 5

Which of the following statements about Gauss’s law is correct?

Accepted Answer

The net electric flux through a closed surface depends only on the net charge enclosed.

Question 6

A solid conductor is in electrostatic equilibrium. Which of the following is true?

Accepted Answer

Any excess charge resides entirely on the surface.

Question 7

A spherical Gaussian surface encloses a point charge $$+q. If $$the radius of the sphere is doubled, what happens to the electric flux through the surface?

Accepted Answer

It remains the same.

Question 8

A closed surface encloses two charges: $$+3\,\mu\mathrm{C}$$ and $$-3\,\mu\mathrm{C}. $$What is the net electric flux through the surface?

Accepted Answer

$$\Phi_E = 0$$

Question 9

A solid metal sphere of radius $$0.450\,\mathrm{m}$$ carries a net charge of $$0.250\,\mathrm{nC}. $$What is the magnitude of the electric field at a point $$0.100\,\mathrm{m}$$ outside the surface?

Accepted Answer

$$E = \dfrac{1}{4 \pi \$$epsilon_0$$} \dfrac{0.250 	imes 10$$^{-9}$$}{(0.550)^2$}$$

Question 10

A conducting spherical shell with inner radius $$a$$ and outer radius $$b$$ has a positive point charge $$Q at $$its center and a total charge $$-3Q on $$the shell. What is the electric field in the region $$a \u003c r \u003c b$$?

Accepted Answer

The electric field is zero.

Question 11

A negative surface charge density exists on a region of a solid conductor. Just beneath the surface, the electric field:

Accepted Answer

Is zero.

Question 12

Which of the following is NOT a property of conductors in electrostatic equilibrium?

Accepted Answer

The electric field just outside the surface is parallel to the surface.

Question 13

A uniformly charged insulating sphere of radius $$R$$ has total charge $$Q. $$What is the electric field at a distance $$r \u003c R$$ from the center?

Accepted Answer

$$E = \dfrac{1}{4 \pi \$$epsilon_0$$} \dfrac{Qr}{R^3$}$$

Question 14

A long, straight wire has a uniform linear charge density $$\lambda. $$Using Gauss’s law, what is the magnitude of the electric field at a distance $$r$$ from the wire?

Accepted Answer

$$E = \dfrac{\lambda}{2 \pi \$$epsilon_0$$ r}$$

Question 15

A parallel-plate capacitor has plates with surface charge densities $$+\sigma$$ and $$-\sigma. $$What is the electric field between the plates?

Accepted Answer

$$E = \dfrac{\sigma}{\$$epsilon_0$$}$$

Question 16

A conducting box (Faraday cage) is placed in a strong external electric field. What is the electric field inside the box?

Accepted Answer

It is zero.

Question 17

Which experiment provided direct evidence for Gauss’s law by showing that charge placed inside a conductor moves to the outer surface?

Accepted Answer

Faraday’s ice pail experiment

Question 18

A closed surface encloses a net charge $$Q. If $$the surface is deformed but still encloses the same charge, what happens to the net electric flux through the surface?

Accepted Answer

It remains the same.

Question 19

A solid conductor contains a cavity with no charge inside. What is the electric field inside the cavity?

Accepted Answer

It is zero.

Gauss’s Law and Electric Flux: Structured Study Notes

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