Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectromagnetic Induction
As shown in the figure, a square frame of wire having a total resistance r is placed coplanarly with a long, straight wire. The straight wire carries a current i given by i = i₀ t . Calculate the heat developed in the frame during the time interval 0 to 20 .
Options
- A5 ₀^2 a^2 i₀^2 2 r ^2 ! (1 + a b )
- B5 ₀^2 a^2 i₀^2 4 r ^2 ! (1 + a b )
- C5 ₀^2 a^2 i₀^2 r ^2 ! (1 + a b )
- D5 ₀^2 a^2 i₀^2 2 ^2 r ^2 ! (1 + a b )
Correct answer
C. 5 ₀^2 a^2 i₀^2 r ^2 ! (1 + a b )
Step-by-step solution
The magnetic field produced by the long straight wire at a distance x is given by B = ₀ i 2 x . Consider an elementary strip of width dx in the square frame at a distance x from the straight wire. The area of this strip is dA = a , dx . The magnetic flux through this elementary strip is d = B , dA = ₀ i a 2 x dx . The total magnetic flux through the square frame is obtained by integrating from x = b to x = b+a : = _ b ^ b+a ₀ i a 2 x dx = ₀ i a 2 [ x]_ b ^ b+a = ₀ i a 2 ( b+a b ) = ₀ i a 2 (1 + a b ) Given the curr