Magnetic field at the centre of a circular lo | vedclass

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

Question

(B) Let $r$ be the radius of the circular loop. The area of the loop is $A = \pi r^{2}$.Therefore,$r = \sqrt{\frac{A}{\pi}}$.The magnetic field $B$ at

Vedclass · Accepted Answer

$\frac{2 B A^{\frac{3}{2}}}{\mu_{0} \pi^{\frac{1}{2}}}$

Vedclass · Answer

(B) Let $r$ be the radius of the circular loop. The area of the loop is $A = \pi r^{2}$.Therefore,$r = \sqrt{\frac{A}{\pi}}$.The magnetic field $B$ at the centre of the circular loop is given by $B = \frac{\mu_{0} I}{2 r}$.Substituting the value of $r$,we get $B = \frac{\mu_{0} I}{2 \sqrt{\frac{A}{\pi}}}$.Solving for current $I$,we get $I = \frac{2 B}{\mu_{0}} \sqrt{\frac{A}{\pi}}$.The magnetic moment $M$ is given by $M = I A$.Substituting the value of $I$,we get $M = \left( \frac{2 B}{\mu_{0}} \sqrt{\frac{A}{\pi}} \right) A$.$M = \frac{2 B}{\mu_{0}} \cdot \frac{A^{1/2}}{\pi^{1/2}} \cdot A = \frac{2 B A^{3/2}}{\mu_{0} \pi^{1/2}}$.

Magnetic field at the centre of a circular loop of area $A$ is $B$. The magnetic moment of the loop will be ($\mu_{0} =$ permeability of free space).

Similar Questions

Curl the palm of your right hand around the circular wire with the fingers pointing in the direction of current and the thumb gives the direction of the magnetic field. In this case,the upper side of the loop may be thought of as

In a hydrogen atom,the electron moves around the nucleus in an orbit of radius $5 \times 10^{-11} \ m$. Its time period is $1.5 \times 10^{-16} \ s$. The current associated with the electron motion is $........$ (charge of electron is $1.6 \times 10^{-19} \ C$)

$A$ closely wound solenoid of $800$ turns and area of cross section $2.5 \times 10^{-4} \text{ m}^2$ carries a current of $3.0 \text{ A}$. The magnetic moment associated with it is . . . . . . . (in $\text{ JT}^{-1}$)

The figure shows a square current-carrying loop $ABCD$ of side $10\,cm$ and current $i = 10\,A$. The magnetic moment $\vec{M}$ of the loop is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module