Electric Fields and Gauss's Law: Master Electrostatics Concepts

Question 1

Dielectric materials possess a permittivity that is:

Accepted Answer

Higher than vacuum.

Answer

Lower than vacuum.

Answer

Equal to vacuum.

Answer

Frequency-dependent.

Question 2

The equipotential surfaces around a point charge are:

Accepted Answer

Spherical.

Answer

Planar.

Answer

Cylindrical.

Answer

Ellipsoidal.

Question 3

A dielectric material with a relative permittivity of 4 has an electric displacement of 2 × 10^-5 C/m². Calculate the electric field strength within the dielectric.

Accepted Answer

5 × 10^5 V/m

Answer

5 × 10^4 V/m

Answer

2.5 × 10^5 V/m

Answer

2.5 × 10^4 V/m

Question 4

Describe the motion of a charged particle released from rest in a uniform electric field.

Accepted Answer

Uniform acceleration

Answer

Constant velocity

Answer

Simple harmonic motion

Answer

Damped oscillation

Question 5

An isolated spherical conductor has a net positive charge (+Q). What is the direction of the electric field outside the conductor?

Accepted Answer

Outward, away from the center of the conductor

Answer

Inward, towards the center of the conductor

Answer

Zero

Answer

Tangential to the surface of the conductor

Question 6

The SI unit of electric potential, defined as the work done per unit charge in bringing a test charge from infinity to a point, is:

Accepted Answer

Volt

Answer

Coulomb

Answer

Farad

Answer

Ohm

Question 7

When a positively charged particle is released from rest in a uniform electric field, it will:

Accepted Answer

Move with increasing acceleration

Answer

Move with constant velocity

Answer

Move with decreasing acceleration

Answer

Remain at rest

Question 8

Which of the following statements about Gauss's law is not true?

Accepted Answer

Gauss's law can be used to find the electric field inside a conductor.

Answer

Gauss's law relates the electric field to the net charge enclosed by a closed surface.

Answer

Gauss's law can be derived from Coulomb's law using the principle of superposition.

Answer

Gauss's law can be used to calculate the electric field of a point charge.

Question 9

What is the characteristic behavior of the electric field created by a point charge?

Accepted Answer

It extends radially outward, decaying in strength with distance

Answer

It follows a circular path, inversely proportional to distance

Answer

It runs parallel to the charge, with a linear relationship

Answer

It possesses an elliptical shape, varying with the charge's polarity

Question 10

For a capacitor with parallel plates separated by distance 'd' and carrying charge 'Q' on each plate, what is the magnitude of the electric field between the plates?

Accepted Answer

Q/(4πε₀d)

Answer

Q/(2ε₀d)

Answer

Q/(4πd)

Answer

Q/(2πd)

Question 11

Which surface geometry is appropriate as a Gaussian surface for calculating the electric field of a line charge using Gauss's law?

Accepted Answer

Cylindrical surface

Answer

Spherical surface

Answer

Elliptical surface

Answer

Conical surface

Question 12

The electric flux through a closed surface enclosing a point charge 'q' is:

Accepted Answer

q/ε₀

Answer

q/2ε₀

Answer

2q/ε₀

Answer

Zero

Question 13

Which statement accurately describes Gauss's law?

Accepted Answer

It relates the electric field to the charge distribution enclosed by a closed surface

Answer

It is only applicable to point charges

Answer

It is expressed as a vector equation

Answer

It is expressed as a scalar equation

Question 14

Which of the following accurately describes the electric field lines generated by a positive point charge?

Accepted Answer

The field lines emanate radially away from the positive charge.

Answer

The field lines form concentric circles around the positive charge.

Answer

The field lines are parallel and equidistant to each other.

Answer

The field lines are perpendicular to the surface of the positive charge.

Question 15

Consider a spherical Gaussian surface with radius 'r' centered on a point charge 'q'. According to Gauss's law, the electric field at a distance 'r' from the charge is given by:

Accepted Answer

q / (4πε₀r²)

Answer

q / (ε₀r²)

Answer

q² / (4πε₀r²)

Answer

q² / (ε₀r²)

Question 16

Which of the following materials has the greatest dielectric constant?

Accepted Answer

Ceramic

Answer

Vacuum

Answer

Air

Answer

Water

Question 17

A parallel-plate capacitor with a capacitance 'C' is connected to a battery with voltage 'V'. The energy stored in the capacitor is given by:

Accepted Answer

1/2 CV²

Answer

CV

Answer

CV²

Answer

1/2 CV

Question 18

The dielectric strength of a material refers to the:

Accepted Answer

Maximum electric field strength that the material can sustain without becoming conductive.

Answer

Minimum electric field strength required to polarize the material.

Answer

Dielectric constant of the material.

Answer

Capacitance of a capacitor made with the material.

Question 19

Gauss's law states that the electric flux through any closed surface is proportional to:

Accepted Answer

The total electric charge enclosed by the surface.

Answer

The area of the surface.

Question 20

Which of the following is a unit of electric field strength?

Accepted Answer

Volt per meter (V/m)

Answer

Coulomb per square meter

Question 21

The electric potential at a point is defined as the:

Accepted Answer

Work done in bringing a unit positive charge from infinity to that point.

Answer

Force experienced by a unit positive charge at that point

Question 22

A parallel-plate capacitor has plates of area A separated by a distance d. If the capacitor is charged to a potential difference V, what is the magnitude of the electric field between the plates?

Accepted Answer

V/d

Answer

Vd/A

Answer

Ad/V

Answer

VA/d

Question 23

Which of the following materials is a good conductor of electricity?

Accepted Answer

Copper

Answer

Glass

Answer

Rubber

Answer

Wood

Question 24

Which of the following accurately describes an electric field?

Accepted Answer

A region of space where electric charges exert forces on each other

Answer

A force acting directly on a point charge

Answer

A potential energy stored within an electric charge

Answer

A flow of electrons

Question 25

Gauss's law establishes a relationship between the electric flux through a closed surface and what physical quantity?

Accepted Answer

Total electric charge enclosed by the surface

Answer

Strength of the electric field at the surface

Answer

Permittivity of the medium within the surface

Answer

Potential difference between the surface and infinity

Question 26

Which material is a proficient conductor of electricity?

Accepted Answer

Copper

Answer

Glass

Answer

Rubber

Answer

Wood

Question 27

Inside a hollow conducting sphere, the electric field is:

Accepted Answer

Zero

Answer

Equivalent to the field outside the sphere

Answer

Proportional to the charge on the sphere

Answer

Inversely proportional to the sphere's radius

Question 28

Which of the following is a practical application of Gauss's law?

Accepted Answer

Calculating the electric field of a charged sphere

Answer

Determining the force between two charged particles

Answer

Measuring the capacitance of a capacitor

Answer

Solving Laplace's equation

Question 29

State Gauss's law, explaining its significance in electrostatics.

Accepted Answer

The net electric flux through any closed surface is directly proportional to the total charge enclosed by the surface.

Answer

The electric flux through a closed surface is proportional to the surface area of the surface.

Answer

The electric field strength at the surface of a closed surface is proportional to the total charge enclosed by the surface.

Answer

The permittivity of the material inside a closed surface is directly proportional to the electric flux through the surface.

Question 30

Calculate the electric flux through a spherical surface of radius 10 cm centered at a point charge of +2 μC placed at the origin.

Accepted Answer

+1.8 x 10^5 Nm²/C

Answer

0 Nm²/C

Answer

-1.8 x 10^5 Nm²/C

Answer

Undefined

Question 31

A conducting sphere of radius R has a charge Q. Determine the electric field strength just outside the surface of the sphere.

Accepted Answer

Qr/(4πε₀r²) N/C

Answer

0 N/C

Answer

Q/(4πε₀rεr) N/C

Answer

Qr/(ε₀r²) N/C

Question 32

Define an electric field.

Accepted Answer

The force per unit charge experienced by a test charge

Answer

A region where electric charges experience a force

Answer

A region where electric charges produce a force

Answer

A region with no electric charges

Question 33

According to Coulomb's law, the electric field strength E due to a point charge q at a distance r is given by:

Accepted Answer

E = k * q / r^2

Answer

E = k * q / r

Answer

E = k * r / q

Answer

E = k * r^2 / q

Question 34

The electric field inside a conductor is:

Accepted Answer

Zero

Answer

Non-zero

Answer

Depends on the shape of the conductor

Answer

Depends on the charge on the conductor

Question 35

The electric field and electric potential are related by:

Accepted Answer

E = -∇V

Answer

E = ∇V

Answer

E = -V∇

Answer

E = V∇

Question 36

Define Gauss's Law mathematically.

Accepted Answer

∮→E⋅d→A=Q/ε0

Answer

→E=∫ρ→dV

Answer

W=−→F⋅→d

Answer

V=∫→E⋅→dl

Question 37

Identify the statement that is not a defining characteristic of electric fields.

Accepted Answer

Electric fields require stationary charges.

Answer

Electric fields are conservative.

Answer

Electric fields obey the superposition principle.

Answer

Electric fields exert non-contact forces.

Question 38

A uniform electric field of 100 N/C is applied along the +x direction. Determine the potential difference between two points 5 cm apart along the x-axis.

Accepted Answer

0.10 V

Answer

0.05 V

Answer

0.15 V

Answer

0.20 V

Question 39

Which material is known for its excellent electrical conductivity?

Accepted Answer

Copper

Answer

Rubber

Answer

Plastic

Answer

Wood

Question 40

Calculate the electric force between two protons separated by a distance of 1 nm.

Accepted Answer

4.6×10^-17 N

Answer

2.3×10^-17 N

Answer

9.2×10^-17 N

Answer

1.8×10^-16 N

Question 41

State the fundamental principle of Gauss's law.

Accepted Answer

The total electric flux through a closed surface is proportional to the net charge enclosed by the surface.

Answer

The electric potential energy of a point charge is proportional to the inverse of the distance from the source charge.

Answer

The electric field at a point is inversely proportional to the square of the distance from the source charge.

Answer

The force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Question 42

Identify an application of Gauss's law.

Accepted Answer

Calculating the electric field of a uniformly charged sphere

Answer

Determining the force between two point charges

Answer

Finding the potential energy of a point charge

Question 43

A point charge of -5 μC is placed at the origin. A Gaussian surface of radius 10 cm is centered at the point (0, 0, 5 cm). Calculate the electric flux through the surface.

Accepted Answer

-9 × 10^5 Nm²/C

Answer

-4.5 × 10^5 Nm²/C

Answer

-1.8 × 10^6 Nm²/C

Answer

0

Question 44

A hollow, conducting sphere of radius R has a net charge Q. Determine the electric field inside the sphere.

Accepted Answer

0

Answer

Q / (4πε₀R²)

Answer

Q / (πε₀R)

Answer

Q² / (4πε₀R²)