A circular conducting coil of radius 1 m being heated by the change of magnetic field B passing perpendicular to the plane in which the coil is laid. The resistance of the coil is 2μΩ. The magnetic field is slowly switched off such that its magnitude changes in time as B = (4/π) × 10?³ T [1 - ( t/100 )]. The energy dissipated by the coil before the magnetic field is switched off completely is E = _______ mJ.
A circular conducting coil of radius 1 m being heated by the change of magnetic field B passing perpendicular to the plane in which the coil is laid. The resistance of the coil is 2μΩ. The magnetic field is slowly switched off such that its magnitude changes in time as B = (4/π) × 10?³ T [1 - ( t/100 )]. The energy dissipated by the coil before the magnetic field is switched off completely is E = _______ mJ.
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1 Answer
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ε = |dΦ/dt| = A|dB/dt|
Given B (t), dB/dt = (4/π) × 10? ³ × (-1/100)
ε = (π × 1²) × | (4/π) × 10? ³ × (-1/100)|
= 4 × 10? V
To find when B=0:
B = 0 ⇒ 1 - t/100 = 0
⇒ t = 100 second
Energy Dissipated, E = P × t = (ε²/R) × t
E = (4×10? )² / (2×10? ) × 100 = 80mJ
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