A long solenoid has n turns per unit length, has a radius R1, and carries a current R2. A circular coil with radius R2 and with N total turns is coaxial with the solenoid and equidistant from its ends. (a) Find the magnetic flux through the coil ifR2 > R1 (b) Find the magnetic flux through the coil if R2 < R1.

a) ∅

b) ∅

Explanation:

The magnetic field inside the solenoid is uniform and the flux in the coil is the same as the flux in the solenoid.

The magnetic field outside can be said to be zero which also means that the flux through the coil is the same as flux in the solenoid.

Thus, we can say

R2 = R1

Where:

N = total turns on coil

n = number of turns per unit length of solenoid

I = current

R1 = radius of solenoid

R2 = circular coil radius

a) The magnetic flux through the coil if R2 > R1 is giben as:

∅

Solving further, we have:

∅

Here,

is the magnetic field

(Pi*R1²) is the area pependicular to magnetic field

N is the number of turns

b) The magnetic flux through the coil if R2 < R1

∅

∅

Here,

is the magnetic field

(Pi*R2²) is the area pependicular to magnetic field

N is the number of turns