What is the statement of Gauss’s Law?
a) The electric field is proportional to the surface charge density
b) The electric flux through any closed surface is proportional to the charge enclosed within that surface
c) The electric potential is inversely proportional to the distance
d) The magnetic field is proportional to the enclosed current
Gauss’s Law is mathematically expressed as:
a) ∮E · dA = ρV
b) ∮E · dA = Q/ε₀
c) ∮E · dA = VQ
d) ∮E · dA = ρ/ε₀
Which of the following is a consequence of Gauss’s Law?
a) Electric fields are always uniform inside a conductor
b) The electric field inside a conductor in electrostatic equilibrium is zero
c) Electric flux is inversely proportional to the charge enclosed
d) The electric potential inside a conductor is non-zero
Gauss’s Law is most useful for calculating electric fields of systems with:
a) Symmetrical charge distributions
b) Asymmetrical charge distributions
c) Time-varying magnetic fields
d) Point charges only
In Gauss’s Law, ε₀ represents:
a) The magnetic constant
b) The electric field strength
c) The permittivity of free space
d) The charge density
Which of the following is an example of a Gaussian surface?
a) A charged wire
b) A spherical surface surrounding a point charge
c) A conductor with current flowing through it
d) A charged plate
For a spherical charge distribution, Gauss’s Law can be used to find the electric field at a distance r from the center if the charge is:
a) Uniformly distributed on the surface of the sphere
b) Concentrated at the center of the sphere
c) Uniformly distributed throughout the volume of the sphere
d) All of the above
If the charge enclosed by a Gaussian surface is zero, the net electric flux through the surface is:
a) Positive
b) Negative
c) Zero
d) Infinite
In Gauss’s Law, the electric field is integrated over the surface. What is the correct form of the differential element for this integration?
a) dA = r² sin(θ) dθ dφ
b) dA = r dθ dφ
c) dA = sin(θ) dθ dφ
d) dA = dθ dφ
In Gauss’s Law, what does the flux depend on?
a) The surface area of the Gaussian surface
b) The charge distribution outside the surface
c) The distance between charges
d) The magnitude of the electric field at the surface
Gauss’s Law is applicable to which of the following types of charge distributions?
a) Spherical
b) Cylindrical
c) Planar
d) All of the above
What is the electric field inside a conductor in electrostatic equilibrium according to Gauss’s Law?
a) Zero
b) Maximum at the surface
c) Constant throughout
d) Varies with distance from the center
In a uniformly charged spherical shell, Gauss’s Law implies that the electric field inside the shell is:
a) Directly proportional to the radius
b) Zero
c) Inversely proportional to the radius
d) Constant throughout
Gauss’s Law can be used to calculate the electric field for which of the following objects?
a) A spherical shell with uniform charge distribution
b) A non-spherical charged body
c) A uniform electric field
d) A charged conductor with irregular shape
What is the result of applying Gauss’s Law to a uniformly charged infinite plane?
a) The electric field is inversely proportional to the distance from the plane
b) The electric field is constant and directed perpendicular to the plane
c) The electric field varies with the square of the distance from the plane
d) The electric field is zero at all points
When a point charge is placed inside a spherical Gaussian surface, the flux is:
a) Directly proportional to the radius of the surface
b) Dependent on the charge enclosed
c) Independent of the shape of the surface
d) Inversely proportional to the distance from the charge
What happens to the electric field when a conductor is placed in an external electric field according to Gauss’s Law?
a) The electric field inside the conductor becomes non-zero
b) The electric field inside the conductor becomes zero
c) The electric field inside the conductor increases
d) The electric field inside the conductor decreases
For an infinitely long charged wire, Gauss’s Law yields an electric field that is:
a) Inversely proportional to the square of the distance
b) Inversely proportional to the distance
c) Directly proportional to the distance
d) Constant at all points
What happens when a dielectric material is inserted between the plates of a parallel plate capacitor according to Gauss’s Law?
a) The capacitance decreases
b) The electric field increases
c) The electric field decreases
d) The electric flux remains the same
What is the net flux through a closed surface with no charge inside, according to Gauss’s Law?
a) Zero
b) Positive
c) Negative
d) It depends on the size of the surface
Gauss’s Law applies to which of the following fields?
a) Gravitational fields
b) Electric fields
c) Magnetic fields
d) Both electric and magnetic fields
In a uniformly charged spherical shell, the electric field outside the shell is:
a) Zero
b) Inversely proportional to the distance squared
c) Constant at all points
d) Directly proportional to the distance
Which of the following would be a valid Gaussian surface for an infinite line of charge?
a) A spherical surface
b) A cylindrical surface
c) A planar surface
d) A cube
When a dielectric is inserted into a capacitor, the electric flux is:
a) Unchanged
b) Reduced
c) Increased
d) Zero
Gauss’s Law is a consequence of which fundamental symmetry?
a) Time symmetry
b) Charge symmetry
c) Rotational symmetry
d) Translational symmetry
The concept of electric flux is related to which of the following?
a) The amount of electric field passing through a given area
b) The total charge in a system
c) The charge on the conducting plates
d) The force on a charged particle
