Question

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. \(E\) is independent of \(r\)	I. For a point charge
B. \(E\) is inversely proportional to \(r\)	II. For a short dipole
C. \(E\) is inversely proportional to \(r^2\)	III. For a uniform line charge
D. \(E\) is inversely proportional to \(r^3\)	IV. For a uniformly charged infinite plane sheet

Choose the correct answer from the options given below:

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

Hint:

Sheet: constant. Line: 1/r. Point: 1/r². Dipole: 1/r³.

Answer 1

The Correct Option is B

Step 1: Method: Count the Powers of r:
Rank the sources by how fast the field dies away. The more spread-out the source, the slower the fall. A plane sheet is the most spread out, then a line, then a point, then a dipole.

Step 2: Assign the Powers:
Sheet: \(r^0\) (constant). Line: \(r^{-1}\). Point charge: \(r^{-2}\). Dipole: \(r^{-3}\), because the two opposite charges partly cancel each other.

Step 3: Read Off the Pairs:
Constant field goes with the sheet: A-IV. \(1/r\) goes with the line: B-III. \(1/r^2\) goes with the point charge: C-I. \(1/r^3\) goes with the dipole: D-II.

Step 4: Find the Option:
Only the second printed option gives A-IV, B-III, C-I, D-II.

Final Answer:
\[\boxed{\text{A-IV, B-III, C-I, D-II (option 2)}}\]