MHT CET20226 Aug 2022Morning ShiftPhysicsElectromagnetic InductionActual
A long solenoid with 15 turns per cm has a small loop of area 2.0 ~cm ^2 placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 Ato 4.0 ~A in 0.1 ~s , the induced emf in the loop while the current is changing is nearly [Take =3.14 ]
Options
- A9 10⁻⁶ ~V
- B4.48 10⁻⁶ ~V
- C5.2 10⁻⁶ ~V
- D7.54 10⁻⁶ ~V
Correct answer
D. 7.54 10⁻⁶ ~V
Step-by-step solution
The magnetic field produced inside the solenoid is B= ₀ n I If A is the area of the loop placed inside the solenoid, then the magnetic flux linked with the loop is given by, =B A= ₀ n I A If e is the induced e.m.f. produced due to change in current through the solenoid, then e=- d d t =- d d t [ ₀ n I A ]=- ₀ n A d I d t Given: Number of turns per unit length of the solenoid, n=15 turns cm ⁻¹=1500 turns m ⁻¹ Given: A=2 ~cm ^2=2 10⁻⁴ ~m ^2 and d I d t = 4-2 0.1 =20 As ⁻¹ e=-4 10⁻⁷ 1500 2 10⁻⁴ 20=-7.54 10⁻⁶ ~V .