Question

Match the LIST-I with LIST-II

• A. A-I, B-II, C-III, D-IV
• B. A-II, B-III, C-IV, D-I
• C. A-IV, B-I, C-III, D-II
• D. A-III, B-IV, C-II, D-I

Hint:

Laplace equation is obtained when charge density is zero.

Answer 1

The Correct Option is D

Concept:
Electrostatics involves equations relating electric field and potential.
Step 1:
Poisson equation is: \[ \nabla^{2}V=-\frac{\rho}{\epsilon_{0}} \] Thus: \[ A \rightarrow III \]
Step 2:
Laplace equation is: \[ \nabla^{2}V=0 \] Thus: \[ B \rightarrow IV \]
Step 3:
Differential form: \[ \nabla\cdot E=\frac{\rho}{\epsilon_{0}} \] \[ C \rightarrow II \] Integral form: \[ \oint E\cdot da=\frac{Q_{enc}}{\epsilon_{0}} \] \[ D \rightarrow I \]
Step 4:
\[ A-III,\quad B-IV,\quad C-II,\quad D-I \] \[ \boxed{\text{Correct Option = (4)}} \]