A current $I$ flows in a long straight wire with cross-section having the form of a thin half-ring of radius $R$ (figure). Find the induction of the magnetic field at the point $O$ .

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

$\frac{μ_{0} i}{π^{2} R}$

$\frac{μ_{0} i}{2 π^{2} R}$

$\frac{μ_{0} i}{2 πR}$

$\frac{μ_{0} i}{4 πR}$

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

Take two elements, as shown in figure. The current in each element,

$d i = \frac{i}{π} d θ$

The resultant field

$B = \int_{0}^{π / 2} 2 \sin θ d B = 2 \int_{0}^{π / 2} (\frac{μ_{0}}{2 π} . \frac{i}{R}) \sin θ d θ = \frac{μ_{0} i}{π^{2} R}$

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE