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

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Given- $B_1 = 2\text{T}$
$B_2 = 1\,\text{T}$
$\Delta t = 10^{-3}\,\text{s}$
$A = 0.01\,\text{m}^2$
$R = 0.01\,\Omega$

Solution - Change in magnetic flux: $\Delta \Phi = (B_1 - B_2) \cdot A = (2 - 1) \cdot 0.01 = 0.01\,\text{Wb}$
Induced EMF: $\text{EMF} = \frac{\Delta \Phi}{\Delta t} = \frac{0.01}{10^{-3}} = 10\,\text{V}$
Induced current: $I = \frac{\text{EMF}}{R} = \frac{10}{0.01} = 1000\,\text{A}$
Heat produced: $H = I^2 R t = (1000)^2 \cdot 0.01 \cdot 10^{-3} = 10\,\text{J}$
Final Answer: ${10\,\text{J}}$

Posted by

Saniya Khatri

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