Derive the equation for the magnetic field at the midpoint between the centers o
ID: 2238207 • Letter: D
Question
Derive the equation for the magnetic field at the midpoint between the centers of the Helmholtz coils. This is the expression given in Eq. (9). Helmholtz coils consist of two coils separated by a distance equal to the coil radius. (You will have to use the above equation twice.) Simplify your answer to a numeric multiple of ?0 iN/R. Clearly 2. From the same starting point as in the previous question, derive the expression for the magnetic field due to Helmholtz coils at the center of one of the coils. Simplify your answer to a numeric multiple of ?0iN/R. show your work. Clearly show your work. 3. Compare the magnetic field strength at the center of one of the coils to the value at the midpoint between the coils. Why are Helmholtz coils useful?
Explanation / Answer
1)..B =magnetic filed at the mid point
=mu*i*R^2N/[2(R^2+R^2/4)^3/2] +mu*i*R^2N/[2(R^2+R^2/4)^3/2] ....
=mu*i*R^2N/[(R^2+R^2/4)^3/2] ....
=mu*i*8R^2N/(5R^2)^3/2 ......
=mu*i*8*R^2N/(125R^3)....
=mu*i*8N/(125R) ....
=(mu*i*N/R)(8/125) .....
2) B1 = magnetic filed at the centre of coil ....
= mu*i*R^2N/[2(R^2+R^2)^3/2] ..
=mu*i*R^2N/[2(2R^2)^3/2] ...
= mu*i*R^2N/[4sqrt(2)R^3] ....
=mu*i*N/[4sqrt(2)R].....
3) B-B1 =(mu*i*N/R)(8/125) - mu*i*N/[4sqrt(2)R] =- (mu*0.11*i*N/R)
comapring ::: magnetic filed at the centre of the coil is more than the magnetic filed at the mid point of the coil ...
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