A fixed horizontal wire carries a current of | vedclass

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

Question

(C) For the second wire to float in air,the downward gravitational force must be balanced by the upward magnetic force exerted by the first wire.$1$.

Vedclass · Accepted Answer

$49\, A$ (direction of current is same to first wire)

Vedclass · Answer

(C) For the second wire to float in air,the downward gravitational force must be balanced by the upward magnetic force exerted by the first wire.$1$. The gravitational force per unit length is $F_g/l = (m/l)g = 10^{-2} 	imes 9.8 = 0.098\, N/m$.$2$. The magnetic force per unit length between two parallel wires is given by $F_m/l = \frac{\mu_0}{4\pi} \cdot \frac{2 i_1 i_2}{a}$.$3$. Equating the two forces: $(m/l)g = \frac{\mu_0}{4\pi} \cdot \frac{2 i_1 i_2}{a}$.$4$. Substituting the values: $10^{-2} 	imes 9.8 = 10^{-7} 	imes \frac{2 	imes 200 	imes i}{2 	imes 10^{-2}}$.$5$. Solving for $i$: $0.098 = 10^{-7} 	imes \frac{400 i}{0.02} = 10^{-7} 	imes 20000 i = 2 	imes 10^{-3} i$.$6$. $i = \frac{0.098}{2 	imes 10^{-3}} = 49\, A$.$7$. Since the magnetic force must be upward (repulsive) to counteract gravity,the currents in the two parallel wires must flow in the same direction.

Similar Questions

An arrangement of three parallel wires placed perpendicular to the plane of the paper,each carrying the same current $I$ in the same direction,is shown in the figure. The magnitude of the force per unit length on the middle wire $B$ is given by:

$A$ square loop $ABCD$ of side $L$ carrying a current $I_1$ is placed at a distance $(L/3)$ from a straight conductor $XY$ carrying current $I_2$. The loop and the conductor are coplanar. The net force on the loop will be ($\mu_0$ = magnetic permeability).

$A$ conducting wire $PQ$ carries a current $10 \ A$ as shown in the figure. It is placed in a uniform magnetic field $5 \ T$ which is acting normally outwards from the paper. The net force experienced by the wire is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module