A conducting rod of length 1m is moved in a magnetic field of magnitude B with velocity v such that the arrangement is mutually perpendicular. Prove that the emf induced in the rod is | E | = Blv.   

Let us assume a rectangular loop LMNO is placed in a uniform magnetic field B.
Suppose at any instant, length ON = x
Flux through the loop, straight ϕ equals space Blx                [because max, flux, straight ϕ space equals BA]
Induced emf,           straight E space equals space minus dϕ over dt space equals space minus straight d over dt Blx
or,                            straight E space equals space minus Bl dx over dt space equals negative Blv

Let us assume a rectangular loop LMNO is placed in a uniform magnetic
where dx over dt space equals space minus straight v comma is the velocity of conductor MN.


277 Views

In the figure given below, a bar magnet moving towards the right or left induces an e.m.f. in the coils (1) and (2). Find, giving reason, the directions of the induced currents through the resistors AB and CD when the magnet is moving (a) towards the left, and (b) towards the right.


(a) When bar magnet is moved towards left, the anticlockwise current will be in loop (1) and (2) {facing bar magnet} following Lenz’s law. Thus, the direction of induced current in loop (1) will be from A to B and that in (2) will be from D to C. 

(b) When bar magnet is moved towards right, the clockwise current will be in loop (1) and (2) {facing bar magnet} following Lenz’s law. Thus, the direction of induced current in the loop (1) will be from B to A and C to D.

846 Views

Advertisement

A coil of number of turns N, area A, is rotated at a constant angular speed ω, in a uniform magnetic field B, and connected to a resistor R. Deduce expressions for:
(i)    maximum emf induced in the coil.
(ii)    power dissipation in the coil.


Given, a coil of N turns having an area A, rotated with angular speed 'ω'  in a uniform magnetic field 'B' connected to a resistor 'R' .
 
The flux linking to the coil,  ϕ = NBA sin (ωt) 
Therefore,
Induced EMF, E = dNBA cos ωtdt    = NBA ω sin ωt  

When, sinωt = ±1, the induced emf value is maximum. 

(i) The maximum EMF, E0 = NBA ω 

(ii) The power dissipated in the coil is given by,  
                 P= E2rmsR   = E022R   = (NAB ω)22R

1514 Views

Advertisement
The loops in the figure move into or out of the field which is along the inward normal to the plane of the paper. Indicate the direction of currents in loops 1, 2, 3,4.



The magnetic flux through the loop in fig. 1 decreases, due to the outward motion of the loop from the magnetic field because, of which the induced current must be clockwise so as to increase the flux. Due to the same reason induced currents in figure 3 and 4 are clockwise.

In figure 2 current must be anticlockwise as flux is increasing because as seen motion of the loop is into the region of the magnetic field.
151 Views

The figure shows two identical rectangular loops (1) and (2) placed on a table along with a straight long current carrying conductor between them.

(i)    What will be the directions of the induced currents in the loops when they are pulled away from the conductor with same velocity v?
(ii)    Will the e.m.f. induced in the two loops be equal? Justify your answer.




(i) The direction of induced current will be such that it tends to maintain the original flux. Therefore, the direction of induced current is anticlockwise in loop 1 and clockwise in loop 2.

(ii) No, the emfs induced in the two loops will not be equal.
Since, the rate of change of flux is more in the second coil, emf induced in the second coil is more than that in the first coil.

Emf in the first coil, E1 = Bav
Emf in the second coil, E2 = Bbv 
Since, b > a therefore, E2 > E1 
904 Views

Advertisement