The ratio of the magnetic field and the magne | vedclass

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

Question

(A) The magnetic field $B$ at the centre of a circular loop of radius $a$ carrying current $I$ is given by $B = \frac{\mu_0 I}{2a}$.The magnetic momen

Vedclass · Accepted Answer

$x / 8$

Vedclass · Answer

(A) The magnetic field $B$ at the centre of a circular loop of radius $a$ carrying current $I$ is given by $B = \frac{\mu_0 I}{2a}$.The magnetic moment $M$ of the loop is given by $M = I A = I(\pi a^2)$.The ratio $x$ is given by:$x = \frac{B}{M} = \frac{\mu_0 I}{2a} 	imes \frac{1}{I \pi a^2} = \frac{\mu_0}{2 \pi a^3}$.When the current $I$ is doubled $(I' = 2I)$ and the radius $a$ is doubled $(a' = 2a)$, the new ratio $x'$ is:$x' = \frac{\mu_0}{2 \pi (a')^3} = \frac{\mu_0}{2 \pi (2a)^3} = \frac{\mu_0}{2 \pi (8a^3)} = \frac{1}{8} \left( \frac{\mu_0}{2 \pi a^3} ight) = \frac{x}{8}$.

The ratio of the magnetic field and the magnetic moment at the centre of a current-carrying circular loop is $x$. When both the current and the radius are doubled, the ratio will be:

Similar Questions

$A$ straight wire carrying a current $I$ is turned into a circular loop. If the magnitude of the magnetic moment associated with it is $M$,then the length of the wire will be

The radius of a circular loop is $r$ and a current $i$ is flowing in it. The equivalent magnetic moment will be

In a hydrogen atom,an electron revolves around the nucleus at a frequency of $6.6 \times 10^{15} \, \text{rev/sec}$ in an orbit of radius $0.528 \, \mathring{A}$. The magnetic moment in $\text{A} \cdot \text{m}^2$ is:

$A$ circular loop has a radius of $5\, cm$ and it is carrying a current of $0.1\, A$. Its magnetic moment is

$A$ closely wound solenoid of $800$ turns and area of cross-section $2.5 \times 10^{-4} \; m^2$ carries a current of $3.0 \; A$. Explain the sense in which the solenoid acts like a bar magnet. What is its associated magnetic moment?

Vedclass Test Series

Exam Paper Generator

Online Exam Module