Here is a homework problem that I am having issues with and an example of the fo

Question

Here is a homework problem that I am having issues with and an example of the format for the answer. Thank you to whoever can help!

Example of Format:

A current of 420 mA is flowing in an ideal solenoid, resulting in a magnetic fleld of 0.040 T. Then the current increases with time, t, according to i)(2.8 vector parallel to tha magnetic field. Fnd the mutual inductanca of the solenoid and the coll and tha Patential difference at3.5 M E rular coil of radius 3.4 cm with N 200 windings is located inside the solenold with its normal

Explanation / Answer

Mutual inductance in the coils is M = µo n N A

Where µo Is permittivity constant = 4pi *10^-7 H/m

A is Area=pi r^2 = 3.14 * 0.034^2 = 0.00362 m^2

N is Number of turns unit length = 200

n is obtained from B = µo n I

n = B/ µoI

n= (0.04)/(4pi *10^-7 * 0.420)

n =7.58 *10^4

so M = (4pi *10^-7 * 7.58 *10^4 * 200 * 0.00362)

M = 0.0689 Henry

Induced voltage V = M di/dt

Given I = Io *(1 + 2.4 t^2)

dI/dt = Io *( 0 + 4.8 t)

dI/dt at time t = 3.5s

dI/dt = 0.420 *(4.8 * 3.5)

dI/dt = 7.056 A/s

so

V = 0.0689 * 7.056

V = 0.486 V or 486 mV

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eXample :

Mutual inductance in the coils is M = µo n N A

Where µo Is permittivity constant = 4pi *10^-7 H/m

A is Area=pi r^2 = 3.14 * 0.034^2 = 0.00362 m^2

N is Number of turns unit length = 200

n is obtained from B = µo n I

n = B/ µoI

n= (0.02)/(4pi *10^-7 * 0.360)

n =4.42 *10^4

so M = (4pi *10^-7 * 4.42 *10^4 * 200 * 0.00362)

M = 0.0402 Henry

Induced voltage V = M di/dt

Given I = Io *(1 + 2.4 t^2)

dI/dt = Io *( 0 + 4.8 t)

dI/dt at time t = 3s

dI/dt = 0.360 *(4.8 * 3)

dI/dt = 5.184 A/s

so

V = 0.0402 * 5.184

V = 0.208 V or 208 mV

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