A thin flexible wire of length L is connected | vedclass

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

Question

(C) Consider a small element of the wire of length $d\ell$ subtending an angle $d	heta$ at the center of the circle formed by the wire.From the geome

Vedclass · Accepted Answer

$\frac{IBL}{2\pi}$

Vedclass · Answer

(C) Consider a small element of the wire of length $d\ell$ subtending an angle $d	heta$ at the center of the circle formed by the wire.From the geometry,$d\ell = R d	heta$,where $R$ is the radius of the circle.The magnetic force on this small element is $dF = B I d\ell = B I R d	heta$,directed radially outwards.This force is balanced by the radial component of the tension $T$ at the two ends of the element.The radial component of tension is $2T \sin(\frac{d	heta}{2})$.For small $d	heta$,$\sin(\frac{d	heta}{2}) \approx \frac{d	heta}{2}$.Equating the forces: $2T (\frac{d	heta}{2}) = B I R d	heta$.$T d	heta = B I R d	heta \Rightarrow T = B I R$.Since the total length of the wire is $L = 2\pi R$,we have $R = \frac{L}{2\pi}$.Substituting $R$ in the expression for tension: $T = B I (\frac{L}{2\pi}) = \frac{IBL}{2\pi}$.

$t$ (in second)	$0$	$2$	$4$	$6$	$8$	$10$
$v$ (in m/s)	$0$	$12$	$16$	$20$	$35$	$60$

Similar Questions

The shortest distance between the lines $r=3i+5j+7k+\lambda(i+2j+k)$ and $r=-i-j-k+\mu(7i-6j+k)$ is

The velocity of a particle which starts from rest is given by the following table. The total distance travelled (in metre) by the particle in $10 \ s$,using the Trapezoidal rule is given by:
$t$ (in second) $0$ $2$ $4$ $6$ $8$ $10$
$v$ (in m/s) $0$ $12$ $16$ $20$ $35$ $60$

If $\cos \theta - 4 \sin \theta = 1$,then $\sin \theta + 4 \cos \theta$ is equal to

The magnetic field at the centre of a circular current-carrying conductor of radius $r$ is $B_c$. The magnetic field on its axis at a distance $r$ from the centre is $B_a$. The value of $B_c : B_a$ will be:

Which of the following is a dihydric alcohol?

Vedclass Test Series

Exam Paper Generator

Online Exam Module