Home
Class 12
PHYSICS
The arm PQ of the rectangular conductor ...

The arm `PQ` of the rectangular conductor is moved from `x=0`, outwards in the uniform magnetic field which extends from `x=0` to `x=b` and is zero for `x gt b` as shown. Only the arm `PQ` possess substantial resistance `r`. Consider the situation when the arm `PQ` is pulled outwards from `x = 0` to `x = 2b`, and is then moved back to `x = 0` with constant speed `v`. Obtain expression for the flux, the induced emf, the force necessary to pull the arm and the power dissipated as Joule heat. Sketch the variation of these quantities with distance.

Text Solution

Verified by Experts

Consider the forward motion from x = 0 to x = 2b. When arem PQ is at x, magnetic flux linked with the circuit PQRS is
`phi = B l x` for `0 le x lt b`
`phi = B l b` for `b le x lt 2 b`
The induced e..m.f. is
`E = (-d phi)/(dt) = - B l v` for `0 le x lt b`
`E = (-d phi)/(dt) = 0` for `b le x lt 2 b`
When the induced e.m.f. in non-zero, the magnitude of current is ` I = (E)/(r) = (B l upsilon)/(r)`
Forcee required to keep the arm PQ in constant motion `= BI l = B((B l upsilon)/(r)) t`
`= (B^(2) l^(2) upsilon)/(r)`, for `0 le x lt b`,
`= zero`, For `b le x lt 2 b`
The direction of the force on PQ is the left.
The joule heating loss is
`P = I^(2) r = (B^(2) l^(2) upsilon)/(r)`, for `0 le x lt b`
`= 0`, for `b le x lt b`
Similar expressions are obtained fro inward motion of PQ from `x = 2 b ti x = 0`. The various quantites have been plotted in fig.
Promotional Banner

Topper's Solved these Questions

  • ELECTROMAGNETIC INDUCTION & ALTERNATING CURRENT

    PRADEEP|Exercise Solved Examples (b)|1 Videos

  • ELECTROMAGNETIC INDUCTION & ALTERNATING CURRENT

    PRADEEP|Exercise Short Answer Qusetions|2 Videos

  • DUAL NATURE OF RADIATION AND MATTER

    PRADEEP|Exercise Exercise|191 Videos

  • ELECTROMAGNETIC WAVES

    PRADEEP|Exercise II Focus multiple choice question|5 Videos

Similar Questions

Explore conceptually related problems

In the following diagram, the arm PQ of the rectangular conductor is moved from x = 0, outwards. The uniform magnetic field is perpendicular to the plane and extends from x = 0 to x = b and is zero for x gt b . Only the arm PQ possesses substantial resistance ‘r’. consider the situation when the arm PQ is pulled outwards from x = 0 to x = 2b, and is then moved back to x = 0 with constant speed ‘ѵ’. Obtain expressions for the (i) electric flux, (ii) the induced emf,(iii)the force necessary to pull the arm and (iv) the power dissipated as Joule heat. Sketch the variation of these quantities with distance.

In the situation shown, the current in arm PQ will be

The area between the arms of the curve |y|=x^(3) from x = 0 to x = 2 is

The arm PQ of a rectangular conductor is moving from x = 0 to x = 2b outwards and then inwards from x = 2b to x = 0 as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from x = 0 to x = b. Identify the graph showing the variation of different quantities with distance :

A conductor PQ , with PQ=r , moves with a velocity v in a uniform magnetic field of induced B . The emf induced in the rod is

In figure, the arm PQ is moved from x = 0 "to" x = 2b with constant speed V. Consider the magnet field as shown in figure. Write (i) direction of induced current in rod (ii) polarity induced across rod.

A conducting rod of length l is moving perpendicular to magnetic field.The rod moves from 0 to 2b while field exists only from 0 to b. Find the graph for emf and power dissipated w.r.t x.