SATHEE: Electro Magnetic Induction And Alternating Currents Question 476

Electro Magnetic Induction And Alternating Currents Question 476

Question: PQ is an infinite current carrying conductor. AB and CD are smooth conducting rods on which a conductor EF moves with constant velocity v as shown. The force needed to maintain constant speed of EF is

Options:

A) $\frac{1}{v R} {[\frac{μ_{0} I v}{2 π} I n, (\frac{b}{a})]}^{2}$

B) ${[\frac{μ_{0} I v}{2 π} I n (\frac{a}{b})]}^{2} \frac{1}{v R}$

C) ${[\frac{μ_{0} I v}{2 π} I n (\frac{b}{a})]}^{2} \frac{v}{R}$

D) $\frac{v}{R} {[\frac{μ_{0} I v}{2 π} I n (\frac{a}{b})]}^{2}$

Show Answer

Answer:

Correct Answer: A

Solution:

Induced emf

$= \int_{a}^{b} B v d x = \int_{a}^{b} \frac{μ_{0} I}{2 π x} v d x$
$\Rightarrow I n d u c e d, e m f = \frac{μ_{0} I v}{2 π} I n (\frac{b}{a})$
$\Rightarrow,$ Power dissipated $= \frac{E^{2}}{R}$

Also, power= $F . v \Rightarrow F = \frac{E^{2}}{v R}$
$\Rightarrow F = \frac{1}{v R} {[\frac{μ_{0} I v}{2 π} I n (\frac{b}{a})]}^{2}$

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Electro Magnetic Induction And Alternating Currents Question 476

Question: PQ is an infinite current carrying conductor. AB and CD are smooth conducting rods on which a conductor EF moves with constant velocity v as shown. The force needed to maintain constant speed of EF is

Options:

Answer:

Solution:

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