Electric Fields and Gauss's Law: Master the Fundamentals of Electrostatics

Question 1

Which material possesses the highest permittivity?

Accepted Answer

Water

Answer

Vacuum

Answer

Air

Answer

Copper

Question 2

Gauss's law establishes a relationship between the electric flux passing through a closed surface and:

Accepted Answer

The total enclosed electric charge.

Answer

The potential difference between the surface and infinity.

Answer

The current density on the surface.

Answer

The capacitance of the surface.

Question 3

The electric field inside a solid conducting sphere is:

Accepted Answer

Zero

Answer

Uniform

Answer

Non-uniform

Answer

Proportional to the charge on the sphere

Question 4

Which law describes the relationship between the electric field at a point and the charge that creates it?

Accepted Answer

Coulomb's law

Answer

Gauss's law

Answer

Ampere's law

Answer

Faraday's law

Question 5

Define the electric potential at a point in space.

Accepted Answer

Work done per unit charge in moving a test charge from infinity to the point

Answer

Force per unit charge at the point

Answer

Electric field at the point

Answer

Potential energy of a charge at the point

Question 6

What is the defining characteristic of an equipotential surface?

Accepted Answer

Constant electric potential

Answer

Zero electric field

Answer

Zero electric charge

Answer

Zero potential energy

Question 7

Describe the primary purpose of a dielectric material.

Accepted Answer

Insulating against electricity effectively

Answer

Conducting electricity efficiently

Answer

Maintaining a high electric field strength

Answer

Exhibiting low magnetic permeability

Question 8

What is the characteristic of the electric field inside a conducting material?

Accepted Answer

Zero

Answer

Non-zero

Answer

Equal to the external electric field

Answer

Opposite to the external electric field

Question 9

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

Accepted Answer

Total charge enclosed by the surface

Answer

Permittivity of the medium inside the surface

Answer

Surface area of the closed surface

Answer

Strength of the electric field just outside the surface

Question 10

Which of the following charge distributions produces a uniform electric field?

Accepted Answer

Infinite plane of charge

Answer

Line of charge

Answer

Sphere of charge

Answer

Point charge

Question 11

Gauss's Law is applicable for determining the electric field of:

Accepted Answer

A conductor in electrostatic equilibrium

Answer

A resistor carrying current

Answer

A dielectric in a non-uniform field

Answer

An inductor with time-varying current

Question 12

Under which condition is the electric flux through a closed surface zero?

Accepted Answer

The surface encloses no net charge

Answer

The surface is in a uniform electric field

Answer

The surface is perfectly conducting

Answer

The surface has a non-zero area

Question 13

The electric displacement vector (D) is related to the electric field (E) and:

Accepted Answer

Polarization of the medium

Answer

Conductivity of the medium

Answer

Permittivity of free space

Answer

Magnetic permeability of the medium

Question 14

Gauss's Law in differential form is expressed as:

Accepted Answer

∇.E = ρ/ε₀

Answer

J = σE

Answer

B.∇ x A = μ₀J

Answer

E = -∇V

Question 15

Gauss's law states that:

Accepted Answer

The net electric flux through any closed surface is proportional to the charge enclosed within the surface.

Answer

The electric field is always perpendicular to the surface of a conductor.

Answer

Gauss's law applies only to charges in vacuum.

Question 16

A hollow conducting sphere has a charge of +10 µC. What is the electric field inside the sphere?

Accepted Answer

0 N / C

Answer

2.25 x 10^9 N / C

Answer

4.5 x 10^9 N / C

Answer

9 x 10^9 N / C

Question 17

A dielectric material with a relative permittivity of 2.5 is inserted between the plates of a capacitor. What is the effect on the capacitance of the capacitor?

Accepted Answer

Increases by a factor of 2.5

Answer

Remains the same

Answer

Decreases by a factor of 2.5

Answer

Decreases by a factor of 0.4

Question 18

In an electric field, the electric potential at a point is given by V. The electric field intensity at that point is:

Accepted Answer

Negative gradient of V

Answer

Zero

Answer

Cannot be determined without more information

Answer

Positive gradient of V

Question 19

A point charge +Q is enclosed by a closed Gaussian surface. The electric flux through the surface is:

Accepted Answer

+Q/ε₀

Answer

-Q/ε₀

Answer

Cannot be determined without knowing the shape of the surface

Answer

0

Question 20

The electric field inside a uniformly charged spherical shell is:

Accepted Answer

Zero

Answer

Proportional to the distance from the center

Answer

Constant and non-zero

Question 21

A non-conducting sphere of radius R carries a charge Q uniformly distributed throughout its volume. The electric field intensity at a point P, a distance r from the center of the sphere, is:

Accepted Answer

Q/(4πε₀r²) if r > R and Q/(4πε₀R³) if r ≤ R

Answer

Zero for all r

Answer

Q/(4πε₀R³) for all r

Answer

Q/(4πε₀R²) for all r

Question 22

The electric field intensity near the surface of a charged conductor is:

Accepted Answer

Proportional to the surface charge density

Answer

Proportional to the volume charge density

Answer

Zero

Answer

Independent of the charge density

Question 23

A point charge Q is placed at the center of a cube of side L. The electric flux through one face of the cube is:

Accepted Answer

Q/6ε₀

Answer

Q/2ε₀

Answer

Q/4ε₀

Answer

Q/ε₀

Question 24

The divergence of the electric field:

Accepted Answer

Is a measure of the net charge density at a point

Answer

Is independent of the charge distribution

Answer

Is zero everywhere

Answer

Is negative in regions with positive charge and positive in regions with negative charge

Question 25

Which of the following statements about electric fields is true?

Accepted Answer

Electric field lines never cross each other

Answer

Electric field lines are closed loops

Answer

The strength of an electric field is inversely proportional to the square of the distance from the source charge

Answer

The electric field due to a point charge is the same in all directions