A circular coil of radius 9 , cm carrying a c | vedclass

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

Question

(B) The torque on a current-carrying coil in a magnetic field is given by $	au = N I A B \sin 	heta$. For small oscillations, $\sin 	heta \approx \

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(B) The torque on a current-carrying coil in a magnetic field is given by $	au = N I A B \sin 	heta$. For small oscillations, $\sin 	heta \approx 	heta$, so $	au = - (N I A B) 	heta$. Comparing this with the equation for simple harmonic motion $	au = -k 	heta$, we get the restoring torque constant $k = N I A B$. The time period of oscillation is $T = 2 \pi \sqrt{\frac{I_{moment}}{k}}$, where $I_{moment}$ is the moment of inertia. Given $T = \frac{1}{3} \, s$, $I_{moment} = 9 	imes 10^{-5} \, kg \cdot m^2$, $B = \pi 	imes 10^{-2} \, T$, $I = 2 \, A$, and $r = 9 \, cm = 0.09 \, m$. The area $A = \pi r^2 = \pi (0.09)^2 = 81 \pi 	imes 10^{-4} \, m^2$. Substituting these values: $\frac{1}{3} = 2 \pi \sqrt{\frac{9 	imes 10^{-5}}{N 	imes 2 	imes 81 \pi 	imes 10^{-4} 	imes \pi 	imes 10^{-2}}}$. Squaring both sides: $\frac{1}{9} = 4 \pi^2 \frac{9 	imes 10^{-5}}{N 	imes 162 \pi^2 	imes 10^{-6}}$. Simplifying: $\frac{1}{9} = \frac{36 \pi^2 	imes 10^{-5}}{N 	imes 162 \pi^2 	imes 10^{-6}} = \frac{36 	imes 10}{162 N} = \frac{360}{162 N}$. Thus, $N = \frac{360 	imes 9}{162} = \frac{3240}{162} = 20$. Therefore, the number of turns is $20$.

Similar Questions

The expression for the torque acting on a coil having area of cross-section $A$,number of turns $n$,placed in a magnetic field of strength $B$,making an angle $\theta$ with the normal to the plane of the coil,when a current $i$ is flowing in it,will be

$A$ circular loop of radius $R$ carries a current $I$. Another circular loop of radius $r (r \ll R)$ carries a current $i$ and is placed at the centre of the larger loop. The planes of the two circles are at right angles to each other. Find the torque acting on the smaller loop.

Vedclass Test Series

Exam Paper Generator

Online Exam Module