First slide

Magnetic flux and induced emf

Question

Figure shows a square loop of side 1m and resistance $1 Ω$ the magnetic field on left side of line PQ has a magnitude B = 1T. The work done in pulling the loop out of the field uniformly in 1s is

Moderate

A

1J
B

10J
C

0.4J
D

100J

Solution

Given side of square loop $l = 1 m$
Time $t = 1 s$
Magnetic field $B = 1 T$
Electro motive force induced in loop due to its velocity
$ε = B l v$
Current $i = \frac{ε}{R} = \frac{B l v}{R}$
$∴ i = \frac{1 \times 1 \times 1}{1} = 1 A$
Work done in pulling the loop is
$\begin{array}{l} W = M [B_{1} - B_{2}] \\ \Rightarrow W = n i A [B_{1} - B_{2}] \\ \Rightarrow W = 1 \times 1 \times 1^{2} [1] \\ ∴ W = 1 J \end{array}$

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