A long solenoid that has 1,140 turns uniformly distributed over a length of 0.415 m produces a magnetic field of magnitude 1.00 10-4 T at its center. What current is required in the windings for that to occur?

Therefore,

Current required is , I

Explanation:

Given:

Turns = N = 1140

length of solenoid = l = 0.415 m

Magnetic Field,

To Find:

Current , I = ?

Solution:

If N is the number of turns in the length, the total current through the rectangle is NI. Therefore, Ampere’s law applied to this path gives

Where,  

B = Strength of magnetic field

l = Length of solenoid

N = Number of turns

I = Current

Therefore,

Substituting the values we get

Therefore,

Current required is , I

if they have a finite resultant

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