Question

A wire carrying current 'I' along x axis has length 'L' and it is kept in a magnetic field \(B(\hat{i}+2\hat{j}-2\hat{k})\) T. The magnitude of magnetic force acting on the wire is

• A. \(\sqrt{8}\,\text{ILB}\)
• B. \(2\,\text{ILB}\)
• C. \(4\,\text{ILB}\)
• D. \(\sqrt{2}\,\text{ILB}\)

Hint:

Force is I L cross B; only the components of B perpendicular to the wire matter.

Answer 1

The Correct Option is A

Step 1: Perpendicular field:
The component of $B$ along the wire is $B$ (the $\hat i$ part) and exerts no force. The perpendicular part is $B(2\hat j - 2\hat k)$.

Step 2: Magnitude of the perpendicular part:
$B\sqrt{4+4} = \sqrt8\,B$.

Step 3: Force:
$F = IL\times\sqrt8\,B$, option (A).

Final Answer:
The force magnitude is root 8 times I L B. \[ \boxed{\text{(A) }\sqrt8\,ILB} \]