Q. A charge Q is uniformly distributed over a spherical surface of radius R. What is the electric field at a point outside the sphere at distance r from the center?
A.0
B.Q/4πε₀r²
C.Q/4πε₀R²
D.Q/4πε₀R
Solution
For points outside the sphere, the electric field behaves as if all the charge were concentrated at the center, so E = Q/4πε₀r².
Q. A charged particle moves from a point of higher electric potential to a point of lower electric potential. What happens to its kinetic energy?
A.Increases
B.Decreases
C.Remains constant
D.Cannot be determined
Solution
As the charged particle moves to a lower potential, it loses potential energy, which is converted into kinetic energy, thus increasing its kinetic energy.
Q. A charged particle moves from a region of high potential to low potential. What happens to its kinetic energy?
A.It increases
B.It decreases
C.It remains constant
D.It becomes zero
Solution
As the charged particle moves from high potential to low potential, it loses potential energy, which is converted into kinetic energy, thus its kinetic energy increases.
Q. A charged sphere has a radius R and a total charge Q. What is the electric potential at a point outside the sphere at a distance r from the center (r > R)?
A.kQ/R
B.kQ/r
C.kQ/(R+r)
D.0
Solution
For a charged sphere, the electric potential outside the sphere behaves as if all the charge were concentrated at the center, so V = kQ/r.
Q. A cylindrical conductor of radius R carries a uniform charge per unit length λ. What is the electric field at a distance r from the axis of the cylinder (r > R)?
A.0
B.λ/(2πε₀r)
C.λ/(2πε₀R)
D.λ/(4πε₀r²)
Solution
For a point outside the cylinder, the electric field is given by E = λ/(2πε₀r).
Q. A cylindrical Gaussian surface encloses a charge Q. If the height of the cylinder is doubled while keeping the radius constant, what happens to the electric flux through the curved surface?
A.It doubles
B.It halves
C.It remains the same
D.It becomes zero
Solution
The electric flux through the curved surface is proportional to the charge enclosed, which remains constant, so the flux through the curved surface doubles if the height is doubled.
Q. A cylindrical Gaussian surface encloses a charge Q. If the radius of the cylinder is r and its height is h, what is the electric flux through the curved surface?
A.Q/ε₀
B.Q/(2ε₀)
C.Q/(4ε₀)
D.0
Solution
The electric flux through the curved surface of a cylinder is given by Φ = Q_enc/ε₀, where Q_enc = Q.
Q. A cylindrical Gaussian surface of length L and radius R encloses a charge Q uniformly distributed along its length. What is the electric field at a distance R from the axis of the cylinder?
A.Q/(2πε₀R)
B.Q/(4πε₀R²)
C.0
D.Q/(ε₀L)
Solution
Using Gauss's law, the electric field outside the cylinder is E = Q/(2πε₀R).
Q. A cylindrical Gaussian surface of length L and radius R encloses a charge Q. What is the electric field E at a distance R from the axis of the cylinder?
A.Q/(2πε₀R)
B.Q/(4πε₀R²)
C.Q/(ε₀L)
D.0
Solution
Using Gauss's law, the electric field E at a distance R from the axis of a long charged cylinder is E = Q/(2πε₀L) for points outside the cylinder.
