Saved Bookmarks
| 1. |
Two concentric circular loops of radius 1 cm and 20 cm are placed coaxially. (i) Find mutual inductance of the arrangement (ii) If the current passed through the outer loop is changed at a rate of 5 A/ms, find the emf induced in the inner loop. Assume the magnetic field on the inner loop to be uniform. |
|
Answer» Solution :(i) Let there be two concentric circular coils of radii r and R respectively. Where R`gtgt`r. If a current `I_(1)` , flows through the outer coil, then magnetic field developed at its centre is `B = (mu_(0)I_(1))/(2 R)` As r is very small, magnetic field on the INNER loop MAY be assumed to be UNIFORM at `B = (mu_(0)I_(1))/(2R)` `:. ` Magnetic flux linked with inner loop `phi_(2) = B(pir^(2))= (mu_(0)I_(1)pir^(2))/(2R) ` `because phi_(2)=MI_(1)`  `:. ` Mutual inductance of the given pair of coils M=` (phi_(2))/(I_(1))=(mu_(0)pir^(2))/(2R)` As per question R =20 cm = 0.2 m and r =1 cm = 0.01 m `:. M =((4pixx10^(-7))xxpixx(0.01)^(2))/(2xx0.2)=9.87xx10^(10)` H (ii) If rate of change of current in outer loop i.e., `(dI_(1))/(dt) = 5 A //ms = 5xx10^(3) A s^(-1)` then magnitude of induced emf in the inner loop is `epsilon_(2) =M (dI_(1))/(dt) = (9.87xx10^(-10))xx(5xx10^(-3))= 4.935 xx10^(-6) V =4.9 mu V` |
|