Question

Suppose that the current in the solenoid is (i(t)). Within the solenoid, but far from its ends, what is the magnetic field (B(t)) due to this current?

a. (B(t) = i(t)r)
b. (B(t) = μ_0 ⋅ i(t)2 π r)
c. (B(t) = μ_0 ⋅ i(t) ⋅ r)
d. (B(t) = μ_0 ⋅ i(t)r^2)

Answer 1

The correct expression for the magnetic field B(t) inside a solenoid is proportional to the current i(t) and involves the number of turns per unit length, making option (b) the correct answer.

Step-by-step explanation:

The magnetic field B(t) inside a solenoid far from its ends can be described by the equation B = μ_0 n I, where μ_0 is the permeability of free space, n is the number of turns per unit length, and I is the current. In this context, the time-dependent current is denoted by i(t). Given the options presented, the correct expression would be option (b), which represents the magnetic field inside the solenoid as proportional to the time-dependent current but does not include the radius or the square of it, rather it's the number of turns per unit length that must be considered.

Therefore, the correct option is neither a, c, nor d, because they propose formulas that either include the radius or its square, or don't feature the number of turns per unit length, which is critical to determining the magnetic field inside a solenoid.