Gauss Law
Q. What is the electric flux through a closed surface surrounding a charge of -3Q?
A.
-3Q/ε₀
B.
3Q/ε₀
C.
0
D.
-6Q/ε₀
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Solution
According to Gauss's law, the electric flux through a closed surface is Φ = Q_enc/ε₀. Here, Q_enc = -3Q, so Φ = -3Q/ε₀.
Correct Answer: A — -3Q/ε₀
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Q. What is the electric flux through a closed surface surrounding a charge Q?
A.
0
B.
Q/ε₀
C.
Q/2ε₀
D.
Q/4ε₀
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Solution
According to Gauss's law, the electric flux Φ through a closed surface is given by Φ = Q/ε₀.
Correct Answer: B — Q/ε₀
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Q. What is the electric flux through a closed surface that encloses no charge?
A.
0
B.
Q/ε₀
C.
Q
D.
4πQ/ε₀
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Solution
According to Gauss's law, if there is no charge enclosed, the electric flux through the surface is zero.
Correct Answer: A — 0
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Q. What is the relationship between electric field E and potential V in a uniform electric field?
A.
E = -dV/dx
B.
E = dV/dx
C.
E = V/dx
D.
E = -V/dx
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Solution
In a uniform electric field, the relationship is given by E = -dV/dx, indicating that the electric field points in the direction of decreasing potential.
Correct Answer: A — E = -dV/dx
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Q. What is the relationship between electric field E and potential V in electrostatics?
A.
E = -dV/dx
B.
E = dV/dx
C.
E = V/dx
D.
E = -V
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Solution
The electric field is the negative gradient of the electric potential, E = -dV/dx.
Correct Answer: A — E = -dV/dx
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Q. What is the relationship between electric field E and surface charge density σ on a conductor?
A.
E = σ/ε₀
B.
E = σ/2ε₀
C.
E = 2σ/ε₀
D.
E = σ/4ε₀
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Solution
The electric field just outside a charged conductor is given by E = σ/ε₀.
Correct Answer: A — E = σ/ε₀
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Q. What is the total electric flux through a closed surface surrounding a charge of -3Q?
A.
-3Q/ε₀
B.
3Q/ε₀
C.
0
D.
-Q/ε₀
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Solution
The total electric flux through a closed surface is given by Φ = Q_enc/ε₀, where Q_enc is the enclosed charge.
Correct Answer: A — -3Q/ε₀
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