Question

A magnetic field of 1 T is acting on a wire carrying a current of 1 A so that the wire is at rest in air. If the mass of the wire is 100 g, then the length of the wire is:

• A. 1 m
• B. 0.5 m
• C. 2 m
• D. 0.25 m

Hint:

When a wire carrying a current is placed in a magnetic field, the magnetic force on the wire is given by \( F_{\text{mag}} = BIL \), and it must balance the weight of the wire for it to be at rest.

Answer 1

The Correct Option is A

The force due to the magnetic field on the wire is: \[ F_{\text{mag}} = BIL \] The weight of the wire is: \[ F_{\text{weight}} = mg \] For the wire to be at rest, the magnetic force must balance the weight of the wire: \[ BIL = mg \] Substitute the values: \[ 1 \times 1 \times L = 0.1 \times 9.8 \] Solving for \( L \): \[ L = \frac{0.1 \times 9.8}{1} = 0.98 \, \text{m} \] Thus, the length of the wire is approximately 1 m.