Home
Class 12
PHYSICS
A long thin wire carrying a varying curr...

A long thin wire carrying a varying current `I = i_(0) sin omegat` lies at a distance `y` above one edge of a rectangular wire loop of length `L and W` lying in the `x-z` plane. What emf is induced in the loop?

Text Solution

Verified by Experts

The correct Answer is:
`(mu_(0))/(4pi)i_(0)W omega cos omega t1n((L^(2) + y^(2))/(y^(2)))`
The magnetic field at point `P` [Fig. S3.27(b)] is
`B = (mu_(0))/(2pi)(i)/sqrt(y^(2) + z^(2))`
The magnetic flux through the shaded strip in Fig. S3.27(a) is
`dphi = (W dz)(mu_(0))/(2pi)(i)/sqrt(y^(2) + z^(2))sin theta`
where `sin theta = (z)/sqrt(y^(2) + z^(2))`
`:.` total magnetic flux through rectangular loop is
`phi = int_(0)^(L)(mu_(0))/(2pi)(i_(0)sin omegat Wzdz)/(y^(2) + z^(2))`
`= (mu_(0))/(4pi)((y^(2) + L^(2))/(y^(2)))i_(0)sin omegat`
(a)
`:.` induced emf in the loop is
`e = (dphi)/(dt) = (mu_(0))/(4pi)i_(0)W omegat 1n((L^(2) + y^(2))/(y^(2)))`
Alternate method to find flux `phi`:
Flux through the given loop will be same as the flux through a cylindrical region from radius `y` to radius `sqrt(L^(2) + y^(2))`

So, `phi = "in"t (mu_(0)i)/(2pix)W dx` `rarr` ` phi = phi = (mu_(0)i)/(2pi)W int _(y)^(sqrt(L^(2) + y^(2)) (dx)/(x)`
`rarr` ` phi = (mu_(0)(i_(0)sin omegat)W)/(2pi)log_(e)[sqrt(L^(2) + y^(2))/(y)]`
`= (mu_(0)W(i_(0)sin omegat))/(4pi)log_(e)[(L^(2) + y^(2))/(y)]`
Now induced emf can be found .
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ELECTROMAGNETIC INDUCTION

    CENGAGE PHYSICS ENGLISH|Exercise Exercises Single Correct|79 Videos

  • ELECTROMAGNETIC INDUCTION

    CENGAGE PHYSICS ENGLISH|Exercise Exercises Multiple Correct|23 Videos

  • ELECTROMAGNETIC INDUCTION

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 3.2|27 Videos

  • ELECTRICAL MEASURING INSTRUMENTS

    CENGAGE PHYSICS ENGLISH|Exercise M.C.Q|2 Videos

  • ELECTRON,PHONTS,PHOTOELECTRIC EFFECT & X-RAYS

    CENGAGE PHYSICS ENGLISH|Exercise dpp 3.3|15 Videos

Similar Questions

Explore conceptually related problems

Find the magnetic field B at the centre of a rectangular loop of length l and width b, carrying a current i.

A square loop of side a is placed in the same plane as a long straight wire carrying a current i . The centre of the loop is at a distance r from wire where r gt gt a . The loop is moved away from the wire with a constant velocity v . The induced e.m.f in the loop is

A wire loop carrying current I is placed in the x-y plane as shown. Magnetic induction at P is

Figure shows a long straight wire carrying current I and a square conducting wire loop of side l, at a distance 'a' from current wire. Both the current wire and loop are in the plane of paper. Find the flux of magnetic filed of current wire, passing through the loop.

Figure shows a long straight wire carrying current , and a square conducting wire loop of side i, at a distance 'a' from current wire. Both the current wire and loop arc in the plane of paper. Find the flux of magnetic field of current wire, passing through the loop.

A rectangular loop carrying a current i_(2) situated near a long straight wire carrying a steady current i_(1) . The wire is parallel to one of the sides of the loop and is in the plane of the loop as shown in the figure. Then the current loop will

A rectangular loop of wire with dimensions shown in figure is coplanar with a long wire carrying current 'I' . The distance between the wire and the left side of the loop is r . The loop is pulled to the right as indicated. What are the directions of the induced current in the loop and the magnetic forces on the left and right sides of the loop when the loop is pulled ?

A square metallic loop of side l is placed near a fixed long wire carrying a current i (figure).The loop is moved towards right perpendicular to the wire with a speed v in the plane containing the wire and the loop.The emf induced in the loop when the rear end of the loop is at a distance a=2l from the wire is (mu_(0)iv)/(xpi) .Find out value of x .

A long wire carrying a steady current I lies in the plane of circular conducting loop placed at a certain distance from the wire. There will be an induced current in the loop if it is

A rectangular loop of wire of size 4 cm xx 10 cm carries a steady current of 2A. A straight long wire carrying 5 A current is kept near the loop as shown. If the loop and the wire are coplanar, find (i) the torque acting on the loop and (ii) the magnitude and direction of the force on the loop due to the current carrying wire.

Home
Profile