Two coils P and Q each of radius R carry curr | vedclass

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

Question

(B) The magnetic field at the centre of a circular coil of radius $R$ carrying current $I$ is given by $B = \frac{\mu_0 I}{2 R}$.For coil $P$ with cur

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) The magnetic field at the centre of a circular coil of radius $R$ carrying current $I$ is given by $B = \frac{\mu_0 I}{2 R}$.For coil $P$ with current $I$,the magnetic field is $\vec{B_P} = \frac{\mu_0 I}{2 R}$.For coil $Q$ with current $\sqrt{8} I$,the magnetic field is $\vec{B_Q} = \frac{\mu_0 \sqrt{8} I}{2 R}$.Since the coils are in perpendicular planes,their magnetic fields $\vec{B_P}$ and $\vec{B_Q}$ are perpendicular to each other.The magnitude of the net magnetic field is $B_{	ext{net}} = \sqrt{B_P^2 + B_Q^2}$.Substituting the values: $B_{	ext{net}} = \sqrt{\left(\frac{\mu_0 I}{2 R}ight)^2 + \left(\frac{\mu_0 \sqrt{8} I}{2 R}ight)^2}$.$B_{	ext{net}} = \frac{\mu_0 I}{2 R} \sqrt{1^2 + (\sqrt{8})^2} = \frac{\mu_0 I}{2 R} \sqrt{1 + 8} = \frac{\mu_0 I}{2 R} \sqrt{9} = \frac{3 \mu_0 I}{2 R}$.

Similar Questions

The figure shows a square loop $ABCD$ with edge length $a$. The resistance of the wire $ABC$ is $r$ and that of $ADC$ is $2r$. The value of the magnetic field at the centre of the loop is:

$A$ cell is connected between the points $A$ and $C$ of a circular conductor $ABCD$ of center $O$ with angle $AOC = 60^o$. If $B_1$ and $B_2$ are the magnitudes of the magnetic fields at $O$ due to the currents in $ABC$ and $ADC$ respectively,the ratio $B_1/B_2$ is

Find the magnetic field at point $O$.

$A$ battery is connected between two points $A$ and $B$ on the circumference of a uniform conducting ring of radius $r$ and resistance $R$. One of the arcs $AB$ of the ring subtends an angle $\theta$ at the centre. The value of the magnetic induction at the centre due to the current in the ring is

Vedclass Test Series

Exam Paper Generator

Online Exam Module