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 2.3 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

Explanation:

The given data is as follows.

 Magnetic field strength (B) = 0.65 T

 Speed (v) = 2.3 m/s

 Induced emf (E) = ?

Formula for emf induced at the ends of the rod of length L which is moving with a speed of v is as follows.

                              E = BvL

Putting the given values into the formula as follows.

          $E_{1} = BvL$

                      = $0.65 T \times 2.3 m/s \times L$

                      = 1.495 L .............. (1)

When magnetic field is changed to $B_{2}$ = 0.48 T

Now, we assume that the speed be $v_{2}$ to get the emf $E_{2} = E_{1}$.

Then,    $0.48 T \times v_{2} \times L = 0.65 T \times 2.3 m/s \times L$

                  $v_{2}$ = 3.11 m/s

Therefore, we can conclude that the speed v of the rod be adjusted to reestablish the emf induced between the ends of the rod at its initial value is 3.11 m/s.