JEE Advanced · Physics · 17. Electrostatics
Which of the following statement(s) is/are correct?
- A If the electric field due to a point charge varies as \(r^{-2.5}\) instead of \(r^{-2}\), then the Gauss's law will still be valid
- B The Gauss's law can be used to calculate the field distribution around an electric dipole
- C If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same
- D The work done by the external force in moving a unit positive charge from point \(A\) at potential \(V_A\) to point \(B\) at potential \(V_B\) is \(\left(V_B-V_A\right)\)
Answer & Solution
Correct Answer
(D) The work done by the external force in moving a unit positive charge from point \(A\) at potential \(V_A\) to point \(B\) at potential \(V_B\) is \(\left(V_B-V_A\right)\)
Step-by-step Solution
Detailed explanation
If charges are of opposite signs, then the two fields are along the same direction. So, they cannot be zero. Hence, the charges should be of same sign.
Therefore, option (c) is correct.
Further, work done by external force = change in potential energy
\(
\begin{aligned}
& \therefore \quad W_{A \rightarrow B}=q(\Delta V) \\
& =(+1)\left(V_B-V_A\right) \\
& \text { or } \quad W_{A \rightarrow B}=V_B-V_A\end{aligned}
\)
Therefore, option (d) is also correct.
\(\therefore\) Correct options are (c) and (d).
Analysis of Question
(i) Question is simple.
(ii) \(W=\Delta U\) (by external force)
If charge is just moved, without changing the kinetic energy. If nothing is mentioned in the question regarding the kinetic energy then we take \(W=\Delta U\).
Therefore, option (c) is correct.
Further, work done by external force = change in potential energy
\(
\begin{aligned}
& \therefore \quad W_{A \rightarrow B}=q(\Delta V) \\
& =(+1)\left(V_B-V_A\right) \\
& \text { or } \quad W_{A \rightarrow B}=V_B-V_A\end{aligned}
\)
Therefore, option (d) is also correct.
\(\therefore\) Correct options are (c) and (d).
Analysis of Question
(i) Question is simple.
(ii) \(W=\Delta U\) (by external force)
If charge is just moved, without changing the kinetic energy. If nothing is mentioned in the question regarding the kinetic energy then we take \(W=\Delta U\).
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