A current of i ampere is flowing in an equilateral triangle of side a . magnetic induction at centro

English

Gujarati

Hindi

4.Moving Charges and Magnetism

medium

A current of $i$ ampere is flowing in an equilateral triangle of side $a$. The magnetic induction at the centroid will be

$\frac{\mu_0 i}{3 \sqrt{3} \pi a}$

$\frac{3 \mu_0 i}{2 \pi a}$

$\frac{5 \sqrt{2} \mu_0 i}{3 \pi a}$

$\frac{9 \mu_0 i}{2 \pi a}$

Solution

(d)

$O$ is centroid and using the $\triangle O A D$ distance $O D=\frac{a}{2 \sqrt{3}}$

By all the three sides $AB , BC$ and $CA$, direction of magnetic field produced will be same and inward to the plane of paper

So $B_{\text {total }}=3\left[\frac{\mu_0 i}{4 \pi\left(\frac{a}{2 \sqrt{3}}\right)}\left(\sin 60^{\circ}+\sin 60^{\circ}\right)\right]=\frac{9 \mu_0 i}{2 \pi a}$

Standard 12

Physics

A rectangular region $A B C D$ contains a uniform magnetic field $B_0$ directed perpendicular to the plane of the rectangle. A narrow stream of charged particles moving perpendicularly to the side $AB$ enters this region and is ejected through the adjacent side $B C$ suffering a deflection through $30^{\circ}$. In order to increase this deflection to $60^{\circ}$, the magnetic field has to be

normal

(KVPY-2021)

An $\alpha -$ particle of $1\,MeV$ energy moves on circular path in uniform magnetic field. Then kinetic energy of proton in same magnetic field for circular path of double radius is……$MeV$

medium

A charged particle of charge $q$ and mass $m$, gets deflected through an angle $\theta$ upon passing through a square region of side $a$, which contains a uniform magnetic field $B$ normal to its plane. Assuming that the particle entered the square at right angles to one side, what is the speed of the particle?

hard

(KVPY-2010)

A particle moving in a magnetic field increases its velocity, then its radius of the circle

easy

What is the behaviour of perpendicular electric field ${\rm{\vec E}}$ and magnetic field ${\rm{\vec B}}$ ?