Question 1

A solid sphere of radius $$r$$ carries a total charge $$Q$$ uniformly distributed throughout its volume. What is the electric field at a point $$P$$ located a distance $$R$$ from the center of the sphere, where $$R \u003e r$$?

Accepted Answer

$$E = \frac{1}{4\pi\$$varepsilon_0$$} \frac{Q}{R^2$}$$

Question 2

Which of the following best describes the direction of the area vector $$\vec{dA}$$ for a flat surface?

Accepted Answer

It is perpendicular to the surface, with direction chosen by the right-hand rule.

Question 3

A fluid flows through a rectangular tube of cross-sectional area $$A$$ with velocity $$\vec{v}. $$What is the flux of the fluid through the cross-section?

Accepted Answer

$$\Phi = vA$$

Question 4

The electric flux through a flat surface of area $$A in a $$uniform electric field $$\vec{E} is $$given by:

Accepted Answer

$$\Phi_E = \vec{E} \cdot \vec{A}$$

Question 5

According to Gauss's Law, the net electric flux through a closed surface is proportional to:

Accepted Answer

The net charge enclosed by the surface.

Question 6

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

Accepted Answer

$$\Phi_E = \frac{q}{\$$varepsilon_0$$}$$

Question 7

If a negative point charge is placed at the center of a spherical Gaussian surface, what is the sign of the net electric flux through the surface?

Accepted Answer

Negative, because the field lines point inward.

Question 8

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

Accepted Answer

The electric field inside the conductor is zero.

Question 9

Where does any excess charge reside on a conductor in electrostatic equilibrium?

Accepted Answer

On the surface of the conductor.

Question 10

A small charged object is placed inside a cavity within a conductor. The conductor itself is electrically neutral. What is the net charge induced on the inner surface of the cavity?

Accepted Answer

Equal in magnitude and opposite in sign to the charge of the object.

Question 11

Which of the following is a property of conductors in electrostatic equilibrium?

Accepted Answer

The surface of a conductor is an equipotential surface.

Question 12

A conducting box is placed in a uniform external electric field. What happens to the electric field inside the box?

Accepted Answer

It becomes zero due to electrostatic shielding.

Question 13

Which of the following materials is an insulator?

Accepted Answer

Glass

Question 14

The SI unit for electric flux is:

Accepted Answer

$$\mathrm{N \cdot m^2$/C}$$

Question 15

If the charge is distributed with a volume charge density $$\rho(x, y, z)$$, the total charge enclosed by a Gaussian surface is:

Accepted Answer

$$q_{enc} = \int\int\int \rho(x, y, z)\, dxdydz$$

Question 16

A Gaussian surface encloses two charges: $$+2\ \mu\mathrm{C}$$ and $$-1\ \mu\mathrm{C}. $$What is the net electric flux through the surface?

Accepted Answer

$$\Phi_E = \frac{1\ \mu\mathrm{C}}{\$$varepsilon_0$$}$$

Question 17

Which of the following statements about the electric field just outside a conductor in electrostatic equilibrium is correct?

Accepted Answer

The electric field is perpendicular to the surface.

Question 18

A semiconductor differs from a conductor in that:

Accepted Answer

It has a smaller band gap than an insulator but larger than a conductor.

Question 19

A closed surface encloses no net charge. According to Gauss's Law, what is the net electric flux through the surface?

Accepted Answer

$$\Phi_E = 0$$

Question 20

Which of the following is NOT a correct application of Gauss's Law?

Accepted Answer

Calculating the electric field at a point near an irregularly shaped charge distribution.

Gauss’s Law and Its Applications in Electrostatics

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