Home
Class 12
PHYSICS
Two concentric circular coils, one of sm...

Two concentric circular coils, one of small radius `r_1` and the other of large radius `r_2`, such that `r_1 lt lt r_2`, are placed co-axially with centres coinciding. Obtain the mutual inductance of the arrangement.

Text Solution

Verified by Experts

Let a current `I_2` flow through the outer circular coil. The field at the centre of the coil is `B_2 = mu_0 I_2 //2r_2` . Since the other co-axially placed coil has a very small radius, `B_2` may be considered constant over its cross-sectional area. Hence,
`Phi_1 = pi r_1^2 B_2`
`= (mu_0 pi r_1^2)/(2r_2)I_2`
`M_(12) I_(2)`
Thus,
`M_(12)= (miu_0 pi r_1^2)/(2r_2)`
From Eq. (6.14)
`M_(12) = M_(21) = (mu_0 pi r_1^2)/(2r_2)`
Note that we calculated M12 from an approximate value of `Phi_1` , assuming the magnetic field `B_2` to be uniform over the area `pi r_1^2`. However, we can accept this value because `r_1 lt lt r_2`.
Doubtnut Promotions Banner Mobile Dark
|

Similar Questions

Explore conceptually related problems

A small circular loop of radius r is placed inside circular loop of radius R (R gt gt r) The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to:

Find the volume of right circular cylinder of base radius r and height 2r .

Knowledge Check

  • Work done in blowing a bubble of radius r is W. Then work done in blowing a bubble of radius 2r is :

    A
    `(W)/(2)`
    B
    2W
    C
    4W
    D
    `2^(2//3)W`.

  • Two circleS of equal radius ' r ' cut orthogonally. If their centres are (2,3) and (5,6), then r=

    A
    1
    B
    2
    C
    3
    D
    4

  • Two circleS of equal radius ' r ' cut orthogonally. If their centres are (2,3) and (5,6), then r=

    A
    1
    B
    2
    C
    3
    D
    4

    • Similar Questions

    Explore conceptually related problems

    If r_1 and r_2 represent radii of two concentric coil (r_2gt gt r_1) then give the expression for the coefficient of mutual inductance for the pair of coils.

    Two identical circular coils are separated by a distance twice the radius of either of the coil. If n = 2, r = 0.08 m, i = 3A, then calculate the resultant magnetic field at the mid point of the line joining their centres, for currents in the same sense and opposite sense in the two circular coils.

    A circular coil of diameter 2 cm and 100 turns is placed at the centre of a long solenoid of radius 5 cm and 10 turns//cm . The mutual inductance of the two coils will be nearest to:

    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_0 IR^2 N)/(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 co-axial 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_0 NI)/(R ) . approximately [Such an arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils.]

    Two concentric coil each of radius 2 pi cm are placed at right angles to each other. Currents of 3A and 4A are passing through them. The magnetic induction in Wb//m^2 at centre of coil is:

    Home
    Profile