Magnetic Field around a Solenoid

Picture given below shows the solenoid. A typical solenoid behaves like a bar magnet. Magnetic field produced by solenoid is constant inside the solenoid and parallel to the axis of it.

solenoid

 

 

 

 

 

 

 

 

 

 

 

 

 

We find the magnetic field produced by solenoid with the following formula;

solenoid  formula

 

 

 

Where: i is the current, N is the number of loops and l is the length of the solenoid.

We find the direction of magnetic field by using right hand rule again. Grab the solenoid as your four fingers shows the direction of current and your thumb shows the direction of magnetic field.

 

Example: Find the magnetic field produced by the solenoid if the number of loop is 400 and current passing through on it is 5 A.( Length of the solenoid is 40cm and k=10-7N/Amps2)

N=400, i=5A, l=40cm=0.4m, k=10-7N/Amps2,

solenoid example

 

 

 

 

 

 

Example: A solenoid has 80 cm diameter, number of loop is 4 and magnetic field inside it is 1,2 .10-5N/Amp.m. Find the current passing through the each loop of wire.

Since the questions ask current on each loop, we assume each loop as circle thus we find the magnetic field;

solenoid example

 

 

 

Example: There are two solenoid given below, they have equal lengths and i1=4Amps and i2=3Amps.  Find the magnetic field vector at point A.

solenoid example

 

 

 

 

 

 

 

 

 

i1 current produces B1 magnetic field and i2 current produces B2 magnetic field. We sum these vectors using vector properties and get following total magnetic field vector at point A.

solenoid example

 

 

 

 

 

 

 

 

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