Question

If a current I is flowing in a loop of radius r as shown in adjoining figure, then the magnetic field induction at the centre O will be

• A. Zero
• B. $\frac{{\mu }_{0}I\theta }{4\pi r}$
• C. $\frac{{\mu }_{0}I\sin \theta }{4\pi r}$
• D. $\frac{2{\mu }_{0}I\sin \theta }{4\pi r^2}$

Answer 1

The correct option is B $\frac{{\mu }_{0}I\theta }{4\pi r}$

Given,

Current flowing in wire $=I$

Radius of wire$=r$

So magnetic field at the centre of loop,

Magnetic field $B=\frac{{\mu }_0}{4\pi }.\frac{2\pi I}{r}$
Here, $2\pi =\theta$
$\therefore B=\frac{{\mu }_0\theta I}{4\pi r}$

So the magnetic field induction at the centre O will $B=\frac{{\mu }_0\theta I}{4\pi r}$