A circular loop having radius r,carrying curr | vedclass

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

Question

(A) The magnetic dipole moment $M$ of a current loop is given by $M = I A$,where $I$ is the current and $A$ is the area of the loop.For a circular loo

Vedclass · Accepted Answer

$\frac{2 \pi B r^3}{\mu_0}$

Vedclass · Answer

(A) The magnetic dipole moment $M$ of a current loop is given by $M = I A$,where $I$ is the current and $A$ is the area of the loop.For a circular loop of radius $r$,the area is $A = \pi r^2$.Thus,$M = I (\pi r^2) \quad \dots(1)$The magnetic field $B$ at the centre of a circular loop carrying current $I$ is given by $B = \frac{\mu_0 I}{2r}$.Rearranging this formula to solve for current $I$,we get $I = \frac{2rB}{\mu_0}$.Substituting the expression for $I$ into equation $(1)$:$M = \left( \frac{2rB}{\mu_0} \right) (\pi r^2)$$M = \frac{2 \pi B r^3}{\mu_0}$.

$A$ circular loop having radius $r$,carrying current $I$,produces a magnetic field at the centre of the loop equal to $B$. What will be the magnetic dipole moment of this loop?

Similar Questions

Two wires of same length are bent to form a circular loop with two turns and a square loop of one turn. Both of them carry the same current. The ratio of the magnetic moment of the circular loop of two turns to that of the square loop is

$A$ circular coil of diameter $7\,cm$ has $24$ turns of wire carrying a current of $0.75\,A$. The magnetic moment of the coil is

$A$ spherical shell of radius $R$ carries a uniformly distributed charge $Q$ and is rotated about its diameter with angular speed $\omega$. Find its magnetic moment.

Two wires of the same length are shaped into a square and a circle. If they carry the same current,the ratio of their magnetic moments is:

The relation between magnetic moment $(M)$ of a current-carrying circular coil and the length $(L)$ of the wire used is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module