The magnetic induction at the centre O is: | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The magnetic field at the centre $O$ due to a circular arc of radius $r$ subtending an angle $	heta$ at the centre is given by $B = \frac{\mu_0 I

Vedclass · Accepted Answer

$\frac{3\mu_0 I}{8a} + \frac{\mu_0 I}{8b} \otimes$

Vedclass · Answer

(D) The magnetic field at the centre $O$ due to a circular arc of radius $r$ subtending an angle $	heta$ at the centre is given by $B = \frac{\mu_0 I 	heta}{4\pi r}$.For the inner arc of radius $a$, the angle subtended is $270^\circ$ or $\frac{3\pi}{2}$ radians. The direction of the magnetic field is inwards $(\otimes)$ by the right-hand rule.$B_1 = \frac{\mu_0 I (3\pi/2)}{4\pi a} = \frac{3\mu_0 I}{8a}$ (inwards).For the outer arc of radius $b$, the angle subtended is $90^\circ$ or $\frac{\pi}{2}$ radians. The direction of the magnetic field is also inwards $(\otimes)$ by the right-hand rule.$B_2 = \frac{\mu_0 I (\pi/2)}{4\pi b} = \frac{\mu_0 I}{8b}$ (inwards).Since both fields are in the same direction, the total magnetic field is:$B = B_1 + B_2 = \frac{3\mu_0 I}{8a} + \frac{\mu_0 I}{8b} \otimes$.

The magnetic induction at the centre $O$ is:

Similar Questions

Two concentric coils of $20$ turns each are placed in the same plane. Their radii are $30 \text{ cm}$ and $60 \text{ cm}$,and they carry $0.4 \text{ A}$ and $0.6 \text{ A}$ currents,respectively,in opposite directions. The magnetic induction at the centre in tesla is ....... .

State the Biot-Savart law.

An electron of mass $m$ is revolving around the nucleus in a circular orbit of radius $r$ and has angular momentum $L$. The magnetic field produced by the electron at the centre of the orbit is ($e = \text{electric charge}$, $\mu_{0} = \text{permeability of free space}$)

The magnetic field at the origin due to the current $I$ flowing in the wire is -

Vedclass Test Series

Exam Paper Generator

Online Exam Module