Question

A conducting rod is moving through a magnetic field, as in the drawing. The magnetic field strength is 0.65 T, and the speed of the rod is 4.8 m/s. Suddenly, the field strength decreases to 0.48 T. To what value must the speed v of the rod be adjusted to reestablish the emf induced between the ends of the rod at its initial value

Answer 1

Answer:

$v_f=6.5\ m.s^{-1}$

Explanation:

Given:

• initial magnetic field, $B_i=0.65\ T$

• speed of the rod initially, $v_i=4.8\ m.s^{-1}$

• final magnetic field, $B_f=0.48\ T$

We know the emf in a moving rod perpendicular to the magnetic field is given as:

$emf=B.l.v$

where:

$l=$ length of the rod

Now the emf has to be constant :

$emf_i=emf_f$

$B_i.l.v_i=B_f.l.v_f$

where:

$v_f=$ final velocity of the rod so that emf remains constant

$0.65\times 4.8=0.48\times v_f$

$v_f=6.5\ m.s^{-1}$