A 100-turn closely wound circular coil of rad | vedclass

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

Question

(C) The magnetic field $B$ at the centre of a circular coil is given by $B = \frac{\mu_0 N I}{2r}$.Given: $B = 3.14 	imes 10^{-3} 	ext{ T}$, $N = 10

Vedclass · Accepted Answer

$2.5 	ext{ A}, 2 	ext{ A m}^2$

Vedclass · Answer

(C) The magnetic field $B$ at the centre of a circular coil is given by $B = \frac{\mu_0 N I}{2r}$.Given: $B = 3.14 	imes 10^{-3} 	ext{ T}$, $N = 100$, $r = 5 	ext{ cm} = 0.05 	ext{ m}$, $\mu_0 = 4\pi 	imes 10^{-7} 	ext{ T m/A}$.Substituting the values: $3.14 	imes 10^{-3} = \frac{4 	imes 3.14 	imes 10^{-7} 	imes 100 	imes I}{2 	imes 0.05}$.$3.14 	imes 10^{-3} = \frac{4 	imes 3.14 	imes 10^{-5} 	imes I}{0.1}$.$10^{-3} = \frac{4 	imes 10^{-5} 	imes I}{0.1} = 4 	imes 10^{-4} 	imes I$.$I = \frac{10^{-3}}{4 	imes 10^{-4}} = \frac{10}{4} = 2.5 	ext{ A}$.The magnetic moment $M$ is given by $M = N I A = N I (\pi r^2)$.$M = 100 	imes 2.5 	imes 3.14 	imes (0.05)^2$.$M = 250 	imes 3.14 	imes 0.0025 = 1.9625 \approx 2 	ext{ A m}^2$.Thus, the current is $2.5 	ext{ A}$ and the magnetic moment is $2 	ext{ A m}^2$.

$A$ $100$-turn closely wound circular coil of radius $5 \text{ cm}$ has a magnetic field of $3.14 \times 10^{-3} \text{ T}$ at its centre. The current flowing through the coil, and the magnitude of the magnetic moment of this coil are, respectively: (Take $\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}$)

Similar Questions

The magnetic field at the centre of a current carrying circular coil of an area $A$ is $B$. The magnetic moment of the coil is (where $\mu_0$ is the permeability of free space).

The magnetic moment of a current $(i)$ carrying circular coil of radius $(r)$ and number of turns $(n)$ varies as

The unit of magnetic moment is . . . . . . .

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 $1.6 \times 10^{-19} \ C$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module