First slide

Magnetic flux and induced emf

Question

A physicist works in a laboratory where the magnetic field is 2 T. She wears a necklace enclosing area 0.01 m² in such a way that the plane of the necklace is normal to the field and is having a resistance R = 0.01 $Ω$ . Because of power failure, the field decays to 1 T in time 10^–3 seconds. Then what is the total heat produced in her necklace ? (T = Tesla)

Moderate

A

10 J
B

20 J
C

30 J
D

40 J

Solution

$\begin{array}{l} H = \frac{V^{2} t}{R} and V = \frac{N (B_{2} - B_{1}) Acos θ}{t} \\ V = \frac{1 \times (1 - 2) \times 0 .01 \times \cos 0^{\circ}}{10^{- 3}} = 10 V \end{array}$
$So, H = \frac{(10)^{2} \times 10^{- 3}}{0 .01} = 10 J$

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