Home
Class 12
PHYSICS
A loop, carring a current i, lying in th...

A loop, carring a current i, lying in the plane of the paper, is in the field of a long straight wire with current `i_0` (inward) as shown in Fig. Find the torque acting on the loop.

Text Solution

Verified by Experts

The correct Answer is:
`(mu_0i_0i)/pi [sin theta](b-a)`
Here the field is tangential at every point on the circular portions
and hence the forces acting on these segments are zero.
Now consider two small elements of length dr at a distance r
from the current element symmetrically as shown in figure.

The magnitude of the force experienced by each element is
`dF=iBdr ( :' dvecF=ivec(dl)xxvecB)`
`{where B=(mu_0i_0)/(2pir)}`
`dF=(mu_0ii_0)/(2pir)dr`
Force on fg will be in inward direction and on eh will be in out-
ward direction.
So, torque about x-axis: `dtau=(2r sin theta)(mu_0i_0i)/(2pir)dr`
To obtain the total torque, we integrate the above expression
within proper limit
`tau=(mu_0i_0i)/pi sin theta int_a^bdr=(mu_0i_0i)/pi[sin theta](b-a)`
Promotional Banner

Topper's Solved these Questions

  • SOURCES OF MAGNETIC FIELD

    CENGAGE PHYSICS ENGLISH|Exercise Exercise (single Correct )|75 Videos

  • SOURCES OF MAGNETIC FIELD

    CENGAGE PHYSICS ENGLISH|Exercise Exercise (multiple Currect )|5 Videos

  • SOURCES OF MAGNETIC FIELD

    CENGAGE PHYSICS ENGLISH|Exercise Concept Exercise 2.2|10 Videos

  • RAY OPTICS

    CENGAGE PHYSICS ENGLISH|Exercise DPP 1.6|12 Videos

  • WAVE OPTICS

    CENGAGE PHYSICS ENGLISH|Exercise Comprehension Type|14 Videos

Similar Questions

Explore conceptually related problems

A wire loop carrying current I is placed in the x-y plane as shown in the figure. If an external uniform magnetic field vec(B)=B hat(i) is switched on, then the torque acting on the loop is

A small current carrying loop having current i is placed in the plane of the paper as shown Another semicircular loop having current i_0 is placed concentrically in the same plane as that of the small loop, the radius of semicircular loop being R(Rgt gt a) . Find the force applied (in newton)by the smaller ring on the bigger ring. (Given R=1m, i=i_0=40/(mu_0)A, a=0.1m)

A closed loop carrying current is placed so that its plane is perpendicular to the long current carrying straight conductor as shown in the figure. The net force acting on the loop is [where WZ and XY are circular arcs)

A current carrying squre loop is placed near an infinitely long current carrying wire as shown in figure . The loop torque acting on the loop is

A square loop of wire carrying current I is lying in the plane of paper as shown in Fig. 1.141. The magnetic field is present in the region as shown. The loop will tend to rotate

A circular loop of radius R=20 cm is placed in a uniform magnetic field B=2T in xy -plane as shown in figure. The loop carries a current i=1.0 A in the direction shown in figure. Find the magnitude of torque acting on the loop.

A circular loop of radius R=20 cm is placed in a uniform magnetic field B=2T in xy -plane as shown in figure. The loop carries a current i=1.0 A in the direction shown in figure. Find the magnitude of torque acting on the loop.

A square loop ABCD , carrying a current I, is placed near and coplanar with a long straight conductor XY carrying a current I.

A rigid square loop of side 'a' and carrying current I_(2) is lying on a horizontal surface near a long current I_(1) carrying wire in the same plane as shown in figure. The net force on the loop to the wire will be :

A square conducting loop is placed in the neighbourhood of a coplaner long straight wire carrying a current i.