Three rings,each having equal radius R,are pl | vedclass

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

Question

(A) The magnetic field at the center of a circular ring of radius $R$ carrying current $I$ is given by $B_0 = \frac{\mu_0 I}{2R}$.Since the three ring

Vedclass · Accepted Answer

$\sqrt{3} \frac{\mu_0 I}{2R}$

Vedclass · Answer

(A) The magnetic field at the center of a circular ring of radius $R$ carrying current $I$ is given by $B_0 = \frac{\mu_0 I}{2R}$.Since the three rings are mutually perpendicular,their magnetic field vectors at the origin will be along the $x$,$y$,and $z$ axes respectively.Let the magnetic fields due to the rings in the $yz$,$zx$,and $xy$ planes be $\vec{B}_x$,$\vec{B}_y$,and $\vec{B}_z$ respectively.Thus,$\vec{B}_x = B_0 \hat{i}$,$\vec{B}_y = B_0 \hat{j}$,and $\vec{B}_z = B_0 \hat{k}$.The resultant magnetic field $\vec{B}$ at the origin is $\vec{B} = \vec{B}_x + \vec{B}_y + \vec{B}_z = B_0 \hat{i} + B_0 \hat{j} + B_0 \hat{k}$.The magnitude of the resultant magnetic field is $B = \sqrt{B_0^2 + B_0^2 + B_0^2} = \sqrt{3 B_0^2} = \sqrt{3} B_0$.Substituting $B_0 = \frac{\mu_0 I}{2R}$,we get $B = \sqrt{3} \frac{\mu_0 I}{2R}$.

Three rings,each having equal radius $R$,are placed mutually perpendicular to each other and each having its centre at the origin of the coordinate system. If current $I$ is flowing through each ring,then the magnitude of the magnetic field at the common centre is

Similar Questions

Which of the following is an example of Disciflorae?

Which of the following is the sweetest sugar?

$540\, g$ of ice at $0^\circ C$ is mixed with $540\, g$ of water at $80^\circ C$. The final temperature of the mixture is

$\int_{-1}^1 (a x^3 + b x) d x = 0$ for

Which of the following plants are used as green manure in crop fields and sandy soils?

Vedclass Test Series

Exam Paper Generator

Online Exam Module