A compact solenoid has length equal to L and number of circular loops equal to N

Question

A compact solenoid has length equal to L and number of circular loops equal to N. The loops are wound around each other such that the innermost windings have radius R1 and outer-most windings have radius R2. Current I flows through the solenoid.

a)Determine an expression for the expected magnitude of the magnetic field at the center of this solenoid (in terms of L, N, I, R1, R2 and µ0).

b) Determine an expression for the expected magnitude of the magnetic field at the entrance of this solenoid (in terms of L, N, I, R1, R2 and µ0) at a point on the central axis of the solenoid.

PLEASE SHOW YOUR WORK!! DO NOT USE AMPERE'S LAW

Explanation / Answer

thus here in Solenoid of length L

integration of B.dL = B L

So

B.L = uo I this is for 1 turn

for N no. of turns

B .L = uo N I

B = uo (N/L) I

B = uo n I

n is no. of turns per unit length

thus Magnetic field of Solenoid Does not depend of Radius R1 and R2

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part B:

Since the part of loop placed inside the Solenoid is acting only on the length L

i.e out of four rpart of rectangular loop, three Contributes to zero mag field

magnetic field Due to Solenoid remains the same B = uo n I

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