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Two identical coils each of radius R and...

Two identical coils each of radius R and each carrying a current I in the same direction are placed along a common axis and separated by distance R. At the midpoint between the two coils the

A

magnetic field is zero

B

magnetic field is 0.8 sqrt(0.8)mu""_0I/R`

C

second derivative of magnetic field

D

first derivative of magnetic field `dB//dx =0`

Text Solution

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The correct Answer is:
B
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Consider two parallel co-axial circular coils of equal radius R, and number of turn N, carrying equal currents in the same direction and separated by a distance R. Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to R, and is given by, B=0.72 (mu_(0)NI)/R , approximately. [Such an arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils.]

For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by B=(mu_0IR^2N)/(2(x^2+R^2)^(3//2)) (a) Show that this reduces to the familiar result for field at the centre of the coil. (b) Consider two parallel coaxial circular coils of equal radius R, and number of turns N, carrying equal currents in the same direction, and separated by a distance R. Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to R and is given by B=0*72(mu_0NI)/(R) approximately. [Such as arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils.]

Knowledge Check

  • Two identical coils are placed coaxially. They carry equal currents in same direction NOTE in parts (a), (b) and (c) exclude the points at infinity.

    A
    on their axis there are two points where net magnetic field is zero
    B
    on their axis there are three points where net magnetic field is zero
    C
    on their axis there is no such point where net magnetic field is zero
    D
    on moving from the centre of one coil to the other, magnetic field will first decrease then increase

  • Two identical coaxial circular loops carry a current i each circulating int the same direction. If the loops approch each other the current in

    A
    each decreases
    B
    each increases
    C
    each remain the same
    D
    one increases whereas that in the other decreases

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