An ideal solenoid of cross-sectional area 10−4 m2 has 500 turns per metre. At the centre of this solenoid, another coil of 100 turns is wrapped closely around it. If the current in the coil changes from 0 to 2 A in 3.14 millisecond, the emf developed in the second coil is
An ideal solenoid of cross-sectional area 10−4 m2 has 500 turns per metre. At the centre of this solenoid, another coil of 100 turns is wrapped closely around it. If the current in the coil changes from 0 to 2 A in 3.14 millisecond, the emf developed in the second coil is
The correct option is D 4 mV
The magnetic field due to the solenoid is
B=μ0nI
where n is the number of turns per unit length. Since the second coil is wrapped closely around the solenoid, the cross-sectional area of the coil can be taken to be equal to that of the solenoid. Since the initial current and hence the initial magnetic field is zero, the change of flux for a single turn is μ0nIA, where A is the cross-sectional area. Therefore, induced emf for a single turn is
|e|=μ0nIAt=4×3.14×10−7×500×2×10−43.14×10−3=4×10−5V∴Induced emf for 100 turns=4×10−5×100=4×10−3=4mV.
4 mV
The magnetic field due to the solenoid is
B=μ0nI
where n is the number of turns per unit length. Since the second coil is wrapped closely around the solenoid, the cross-sectional area of the coil can be taken to be equal to that of the solenoid. Since the initial current and hence the initial magnetic field is zero, the change of flux for a single turn is μ0nIA, where A is the cross-sectional area. Therefore, induced emf for a single turn is
|e|=μ0nIAt=4×3.14×10−7×500×2×10−43.14×10−3=4×10−5V∴Induced emf for 100 turns=4×10−5×100=4×10−3=4mV.
