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:
A, B, C, D
`(di)/(dt)=l_(@)omega cos omegat B=(mu_(0)i)/(2pi(y^(2)+z^(2))^(1//2))`
`dphi=B(dA)cos theta =B(W dz)cos theta =(mu_(0)i)/(2pi(y^(2)+z^(2))^(3/2)) (W dz) cos theta`
`phi=(mu_(0)iW)/(2pi)underset(0)overset(L)intZ/(y^(2)+z^(2))dz =(mu_(0)iW)/(4pi)[ln(y^(2)+z^(2))]_(0)^(L) =(mu_(0)iW)/(4pi)ln[(y^(2)+L^(2))/y^(2)]`
`epsilon=(dphi)/(dt)= =(mu_(0)iW)/(4pi)ln[(y^(2)+L^(2))/y^(2)] (di)/(dt)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ELECTROMAGNETIC INDUCTION

    RESONANCE|Exercise Exercis-3 PART 3|16 Videos

  • ELECTRODYNAMICS

    RESONANCE|Exercise Advanced level problems|31 Videos

  • ELECTROSTATICS

    RESONANCE|Exercise HLP|39 Videos

Similar Questions

Explore conceptually related problems

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 long straight wire carries a current I=I_(0) sin (omegat+del) and lies in the plane of a rectangular loop of N turns of wire as shwon in figure-5.351. The quantities l_(0) omega and del are all constants. Determine the EMF induced in the loop by the magnetic field due to the current in the straight wire. Assume I_(0)=50A,omega=200pi//s,N=100,a=b=5cm cm and l=20cm.

Knowledge Check

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

    A
    `(mu_(0) I)/(2a) ((sqrt(3))/(pi) - (1)/(3))`
    B
    `(mu_(0) I)/(2a) ((1)/(3) - (pi)/(sqrt(3)))`
    C
    `(mu_(0)I)/(2a) ((1)/(3) + (sqrt(3))/(pi))`
    D
    `(mu_(0)I)/(2a) ((sqrt(3))/(pi) - (1)/(3))`

  • A rectangular loop of wire with dimensions shown in figure is coplanar with a long wier 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
    `{:(,"Induced Current","Force on Left side","Force on Right side",,),(a,"Currentclockwise","To the left","To the left",,):}`
    B
    `{:(,"Induced Current","Force on Left side","Force on Right side",,),(b,"Currentclockwise","To the right","To the left",,):}`
    C
    `{:(,"Induced Current","Force on Left side","Force on Right side",,),(c,"Clockwise","To the right","To the left",,):}`
    D
    `{:(,"Induced Current","Force on Left side","Force on Right side",,),(d,"Clockwise","To the left","To the right",,):}`

  • A long straight wire carrying current I and a square conducting wire loop of side l , at a distance 'a' from current wire as shown in the figure. Both the current wire and loop are in the plane of paper. Find the magnetic flux of current wire, passing through the loop.

    A
    `(mu_(0))/(2pi).Illog_(e).(a+I)/(a)`
    B
    `(mu_(0))/(4pi).Illog_(e).(a+I)/(a)`
    C
    `(mu_(0))/(2pi).Il`
    D
    `(mu_(0))/(4pi).I`

    • Similar Questions

    Explore conceptually related problems

    A square meallic 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 .

    Consider a long infinite wire carrying a time varying current i=kt(kgt0) . A circular loop of radius a and resistance R is placed with its centre at a distance d from the wire (altltd) . Find out the induced current in the loop?

    A long wire carrying current i_(0) is planced near a small cube of edge a at distance d(d gt gta) . Find the magnetic energy stored in 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 shown below is coplanar with a long wire carrying current I. 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 the right sides of the loop

    Home
    Profile