In the figure below a 150 turn coil of radius 20 cm and res

In the figure below a 150 - turn coil of radius 2.0 cm and resistance 1.6 ohm is coaxial with a solenoid with 250 turns/cm and diameter 3.0 cm. The solenoid current drops uniformly from 4.5 A to zero in time interval delta t = 15 ms. During this time delta t calculate: The current induced in the coil. The magnitude of E field at r = 1.0 cm from the axis of the solenoid. The magnitude of E field at r = 3.0 cm from the axis of the solenoid.

Solution

As the magnitude of the current changes, the net flux through the coil changes, hence inducing an EMF in the circuit.

Part A.) Her the emf induced woul be given as: d / d t   

where flux = = B.A = _onIR²

SO the EMF induced = d / d t = 4 x 3.14 x 10^-7 x 250 x 4.5 x 3.14 x 0.015² / 15 x 10^-3 = 0.666 x 10^-4 Volts

Net emf for 150 turns of the coil = 99.828 x 10^-4 Volts

Therefore current = EMF/ Resistance = 99.828 x 10^-4 / 1.6 = 62.393 x 10^-4 Volts

Part B.) For a changing magnetic flux, we have the relation as:

E . dl = d / d t

Now for r = 1 cm, the flux would be: _onIr²

So, we get: E(2r ) = _onr² dI/dt

or, E = (_on r / 2) dI/dt

So, we get the required electric field as E = 2 x 3.14 x 10^-7 x 250 x 0.01 x 4.5 / 15 x 10^-3 = 4.71 x 10^-4 N/C

Part c.) Again applying the same relation as above, we get:

E(2r ) = _onR² dI/dt

or, E = (_onR²/2r) dI/dt = 2 x 3.14 x 10^-7 x 250 x 0.015² x 4.5 / 2 x 0.03 x 15 x 10^-3

Therefore the required electric field is given as: E = 1.76625 x 10^-4 N/C