Picture given below shows the solenoid. A typical solenoid behaves like a bar magnet. Magnetic field produced by the solenoid is constant inside the solenoid and parallel to the axis of it.
![](https://lh3.googleusercontent.com/-6EmV5MW_Xuw/VpizQRcrIJI/AAAAAAAALMk/lHNMdKHaK-A/s323-Ic42/1.png)
We find the magnetic field produced by solenoid with the following formula;
![](https://lh3.googleusercontent.com/-mVHVXdwgT0I/VpizQ489ISI/AAAAAAAALLw/QZUrEkxcBts/s112-Ic42/2.png)
Where: i is the current, N is the number of loops and l is the length of the solenoid.
We find the direction of a magnetic field by using right-hand rule again. Grab the solenoid as your four fingers show 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 loops 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,
![](https://lh3.googleusercontent.com/-NqbTHB7Pzjo/VpizRG4z7gI/AAAAAAAALLI/nL1_9eJQxDM/s267-Ic42/3.png)
Example: A solenoid has 80 cm diameter, the number of loops 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;
![](https://lh3.googleusercontent.com/-Dl_QzN_juVE/VpizRjkJuuI/AAAAAAAALL0/c_W0-UiD0E8/s543-Ic42/4.png)
Example: There are two solenoids given below, they have equal lengths and i1=4Amps and i2=3Amps. Find the magnetic field vector at point A.
![](https://lh3.googleusercontent.com/-toGaNLLCqvw/VpizR_ttyTI/AAAAAAAALLk/-brFY25i0B8/s303-Ic42/5.png)
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.
![](https://lh3.googleusercontent.com/-PrnUaXJ-5IU/VpizSF_9o3I/AAAAAAAALL8/UOKmc0YrGig/s161-Ic42/6.png)
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