JEE Mains · Physics · STD 12 -6. Electromagnetic induction
A rectangular loop of sides \(12 \mathrm{~cm}\) and \(5 \mathrm{~cm}\), with its sides parallel to the \(x\)-axis and \(y\)-axis respectively moves with a velocity of \(5 \mathrm{~cm} / \mathrm{s}\) in the positive \(\mathrm{x}\) axis direction, in a space containing a variable magnetic field in the positive \(z\) direction. The field has a gradient of \(10^{-3} \mathrm{~T} / \mathrm{cm}\) along the negative \(\mathrm{x}\) direction and it is decreasing with time at the rate of \(10^{-5} \mathrm{~T} / \mathrm{s}\). If the resistance of the loop is \(6 \mathrm{~m} \Omega\), the power dissipated by the loop as heat is _______ \(\times 10^{-9} \mathrm{~W}\).
- A \(215\)
- B \(216\)
- C \(217\)
- D \(218\)
Answer & Solution
Correct Answer
(B) \(216\)
Step-by-step Solution
Detailed explanation
\(\mathrm{B}_0\) is the magnetic field at origin \(\frac{d B}{d x}=-\frac{10^{-3}}{10^{-2}}\) \(\int_{B_0}^B d B=-\int_0^x 10^{-1} d x\) \(B-B_0=-10^{-1} x\) \(B=\left(B_0-\frac{x}{10}\right)\) Motional emf in \(\mathrm{AB}=0\) Motional emf in \(\mathrm{CD}=0\) Motional emf in…
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