Question

This is Physics 2, College Level: Someone answered wrong so take your time, do not rush to answer these questions. Explain how you got the answers.

A 1.00 F capacitor is charged to 6.00 V. The capacitor and an open switch is connected to a coil of wire that consists of 500 windings, which has a resistance of 1.20 Ω. This coil has a diameter of 5.00 cm and a length of 16.0 cm. A slightly smaller coil is placed inside the larger coil. The smaller coil is 2000 windings, 4.50 cm in diameter, and 16 cm long. This smaller coil has a resistance of 8.00 Ω. At t = 0 s the open switch is closed and the capacitor begins discharging through the larger coil. This leads to a changing voltage, current, magnetic field, and magnetic flux in the outer coil, which induces an Emf in the inner coil. Find the following quantities.

What will be the maximum value of the magnetic field inside the outer coil? B_{max =} ________micro Tesla (mT)

What will be the maximum induced emf across the inner coil? Vmax = _________micro Volts(mV).

What will be the induced emf across the inner coil 1.00 s after the switch is closed? V_{max = _________micro Volts(mV).}

Answer 1

1) As we know that when a capacitor discharges across a resistance in series with it the Voltage across the circuit can be given by

Now as we know that maximum voltage is V

so V_{o}= 6

and the resistance of the circuit i,e soleniod is 1.2 ohms

and capacitance is 1.0 F

So equation reduce to

Now magnetic field inside the outer coil will be given by

Now magnetic field will be maximum when current through coil is maximum  

curent through the ciruit will be given by

=>

Now i will be maximum when t=0

I _{maximum}=5

By calculation

B=19625 microTesla

2) Note that the EMF inducced will be due to mutual inductance of the the coils and the rate of change of the current

by calculation mutual inductance will be given a by

M=12.47 mH

Now di/dt will be given by

Emf will be

now emf will be max when di/dt will be max

di/dt(max)=-25/4

Emf(max)=7799 micro Volts

31) similarly for emf after 1 seconds

we have to just calculate the di/dt after 1 second

which will be equal to

di/dt(1 second)=2.7292

Emf(1 second) 3471 micro Volts