A wire of cross-sectional area A forms three sides of a square and is free to rotate about axis OO1 . If the structure is deflected by an angle θ from the vertical when current i is passed through it in a magnetic field B acting vertically upwards and density of the wire is ρ , then the value of θ is given by

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

2AρgiB=cotθ

2AρgiB=tanθ

AρgiB=sinθ

Aρg2iB=cosθ

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Let a is the side of square.Torque of current = MB=sin(90−θ)=MBcosθ=ia2BcosθMass of each side= m=ρAaTorque of gravity = 2mga2sinθ+mg a sinθ =2mg a sinθ=2ρAga2sinθNow, at equilibrium both torques should be samei.e., ia2Bcosθ=2ρAga2sinθ⇒ cotθ=2ρAgiB .

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th