Two parallel coaxial circular coils of radius r and equal number of turns and carry equal current i in the same direction and are separated by a distance to find the magnitude and direction of the net magnetic field produced at the midpoint of the line joining the centre
Answers
Answer:
B = (μoNIR^2) /8R^3.
Step-by-step explanation:
If we let that the radius of the given 2 parallel co-axial circular coil will be R .
The number of turns of the coil will be N while the current flowing through the coil will be I and the distance of separation between the two coils be 2R.
Since, from the question we know that the point of finding the magnets field is half distance of the two coils separation, which is at R from centers of both the coils.
If amgnetic field for coil 1 is B1 then,
So, B1 = (μoNIR^2) / 2[(R+R)^2+R]^3/2 .
So, for the other B2 = (μoNIR^2) / 2[(R+R)^2+R]^3/2 .
Therefore, total magnetic field will be,
B = B1 + B2 .
B= (μoNIR^2) / 2[(R+R)^2+R]^3/2 + (μoNIR^2)/2[(R+R)^2+R]^3/2
= (μoNIR^2)/[(R+R)^2+R]^3/2
= (μoNIR^2) / [4R^2+R]^3/2
= (μoNIR^2) /8R^3[1+1/R]^3/2
We also know that R is very very large than 1 so the value of total magnetic field B will be:-
B = (μoNIR^2) /8R^3.