# Solenoid Formula

A solenoid is a coil of wire through which a current flow. The magnetic field is determined by the contribution of each loop in the solenoid, so the total magnetic field is dependent on the number of turns and the length of the solenoid. The formula is

Magnetic field = magnetic permeability * current *(Number of turns / Length of the solenoid)

The equation is:

B = μ I N/L

Where:

μ: permeability

B: magnetic field

I: current intensity flowing in the cable

N: number of turns of the wire

L: Length of the solenoid

Solenoid Formula Questions:

1) A solenoid of 30 cm length carries a current I= 2 A. If the number of turns is 300, what is the magnetic field inside the solenoid?

Answer:

From the formula of the magnetic field inside the solenoid we substitute the values,

B = μ I N/L = 4π *10^{(-7)} T*m/A * 2 A * 300/30 cm

= 4π *10^{(-7)} T*m/A * 2 A * 300/0.3 m

= 2.5*10^{(-3)} T

2) A solenoid of 30 cm length carries a current I= 2 A. If the magnetic field is of 4*10^{(-3)} T, what number of turns of the solenoid?

Answer:

From the formula of the magnetic field inside the solenoid we find the number of turns,

N= B L/μ I = 4 *10^{(-3)} T * 0.3 m/ (4π *10^{(-7)} T*m/A* 2A)

N= 0.04 * *10^{(4)} = 400

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