Question

Diagram shows a circular loop of radius r and resistance R. A variable magnetic field of induction B = B₀e^–t is established inside the coil. If the key K is closed, the power developed in the coil just after closing the key-

• A.
• B.
• C.
• D. $\frac { \mathrm { B } _ { 0 } { } ^ { 2 } \pi ^ { 2 } \mathrm { r } ^ { 4 } } { \mathrm { R } }$

Answer 1

Answer: (D)

$\frac { \mathrm { B } _ { 0 } { } ^ { 2 } \pi ^ { 2 } \mathrm { r } ^ { 4 } } { \mathrm { R } }$

Answer 2

E_in = A $\frac { \mathrm { dB } } { \mathrm { dt } }$ = pr²B₀ = (pr²e^–t B₀)

\P = $\frac { \mathrm { B } _ { 0 } ^ { 2 } \pi ^ { 2 } \mathrm { r } ^ { 4 } } { \mathrm { R } } = \mathrm { P }$