A compact solenoid has length equal to L and number of loops equal to N. The loo

Question

A compact solenoid has length equal to L and number of 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). You can use the expression for the field at the center of a compact solenoid (R=constant) described in the magnetic fields lab activity as a starting point. b) Using the expression from part (a), calculate the expected field (in T) at the center of a compact solenoid having N=3400, L = 0.089 m, R1=0.046 m, R2 = 0.62 m, and I = 1.00 A.

Explanation / Answer

length = L
inner radius = R1
outer radius = R2

a) B inside a solenoid = mu*NI/L
Now for a thich solenoid, number of loops in each layer of solenoid = N
thickness of wire = d
Nd = L
and number of layers = n
n*d = R2 - R1
Net B = mu*(L/d)(R2 - R1)/d *I/L
B = mu*(R2 - R1)*I/d^2
but, d = (L/N)
so B = mu*(R2 - R1)*I*N^2/L^2

b) B = 10^-7*(0.62-0.046)*1*3400^2 / 0.089 *4*3.14 = 0.59359 T

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