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

The work done by a force $\vec F = (-6x^3 \hat i) \, N$,in displacing a particle from $x = 4 \, m$ to $x = -2 \, m$ is ................ $J$.

$A$ satellite is launched into a circular orbit of radius $R$ around the Earth,while a second satellite is launched into an orbit of radius $1.02 R$. The percentage difference in the time periods of the two satellites is ......... $\%$

$A$ metal rod of length $2 \text{ m}$ has cross-sectional areas $2A$ and $A$ as shown in the figure. The ends are maintained at temperatures $100^{\circ}\text{C}$ and $70^{\circ}\text{C}$. The temperature at the middle point $C$ is...... $^{\circ}\text{C}$

These are regarded as major causes of biodiversity loss :
$A.$ Over-exploitation
$B.$ Co-extinction
$C.$ Mutation
$D.$ Habitat loss and fragmentation
$E.$ Migration
Choose the correct option :

$A$ radioactive sample $S_1$ having an activity of $5\,\mu Ci$ has twice the number of nuclei as another sample $S_2$ which has an activity of $10\,\mu Ci$. The half-lives of $S_1$ and $S_2$ can be

Vedclass Test Series

Exam Paper Generator

Online Exam Module