The magnetic field existing in a region is gi | vedclass

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

Question

(C) The magnetic field is $\vec{B} = 0.2(1 + 2x) \hat{k} 	ext{ T}$. The loop is a square with side length $L = 0.5 	ext{ m}$. The loop is placed fro

Vedclass · Accepted Answer

$50$

Vedclass · Answer

(C) The magnetic field is $\vec{B} = 0.2(1 + 2x) \hat{k} 	ext{ T}$. The loop is a square with side length $L = 0.5 	ext{ m}$. The loop is placed from $x = 2 	ext{ m}$ to $x = 2.5 	ext{ m}$ and $y = 2 	ext{ m}$ to $y = 2.5 	ext{ m}$.For the segments parallel to the $x$-axis,the forces are equal and opposite,so they cancel out.For the segments parallel to the $y$-axis,the force is given by $\vec{F} = I \int (d\vec{l} 	imes \vec{B})$.At $x = 2 	ext{ m}$,the current flows in the negative $y$-direction: $\vec{F}_1 = I L \hat{j} 	imes \vec{B}(x=2) = 0.5 	imes 0.5 	imes [0.2(1 + 2(2))] \hat{j} 	imes \hat{k} = 0.25 	imes 1 \hat{i} = 0.25 	ext{ N}$ (in $+x$ direction).At $x = 2.5 	ext{ m}$,the current flows in the positive $y$-direction: $\vec{F}_2 = I L (-\hat{j}) 	imes \vec{B}(x=2.5) = 0.5 	imes 0.5 	imes [0.2(1 + 2(2.5))] (-\hat{j}) 	imes \hat{k} = 0.25 	imes 1.2 (-\hat{i}) = -0.30 	ext{ N}$ (in $-x$ direction).The net force is $F_{	ext{net}} = |F_1 - F_2| = |0.25 - 0.30| = 0.05 	ext{ N} = 50 	ext{ mN}$.

Similar Questions

$A$ loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the magnetic force acting on the wire.

$A$ wire carrying a current $i$ is placed in a uniform magnetic field $B$ in the form of the curve $y = a \sin \left( \frac{\pi x}{L} \right)$,where $0 \leq x \leq 2L$. The magnetic force on the wire is

The force between two long parallel wires is $F$ when each one of them carries a certain current $I$. If the current in each is halved,the force between them would be . . . . . . .

$A$ uniform conducting wire $ABC$ has a mass of $10 \, g$. $A$ current of $2 \, A$ flows through it. The wire is kept in a uniform magnetic field $B = 2 \, T$. The acceleration of the wire will be ............. $m \, s^{-2}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module