Two identical coils having radius R and number of turns N are placed co-axially with their centres separated by a distance equal to their radius R. The two coils are given same current I in same direction. The configuration is often known as a pair of Helmholtz coil. (i)Calculate the magnetic field (B) at a point (P) on the axis between the coils at a distance x from the centres of one of the coils. (ii)Prove that(dB)/(dx) = 0 and(d^(2)B)/(dx^(2)= 0[ In fact(d^(3)B)/( dx^(3))is also equal to zero ]at the point lying midway between the two coils. What conclusion can you draw from these results?

Two identical coils having radius R and number of turns N are placed c

1.	Two identical coils having radius R and number of turns N are placed co-axially with their centres separated by a distance equal to their radius R. The two coils are given same current I in same direction. The configuration is often known as a pair of Helmholtz coil. (i)Calculate the magnetic field (B) at a point (P) on the axis between the coils at a distance x from the centres of one of the coils. (ii)Prove that(dB)/(dx) = 0 and(d^(2)B)/(dx^(2)= 0[ In fact(d^(3)B)/( dx^(3))is also equal to zero ]at the point lying midway between the two coils. What conclusion can you draw from these results?
Answer» ANSWER :`(1) (mu_(0)NIR^(2))/2[1/((R^(2)+x^(2))^(3//2)+1/[R^(2)+(R-x^(2)]^(3//2)]` (2) The magnetic field is constant at POINTS CLOSE to mid way between the COILS.

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