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 4.2 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?

5.69 m/s.

Explanation:

The given data is as follows.

 Magnetic field strength (B) = 0.65 T

 Speed (v) = 4.2 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.

.

When magnetic field is changed to

Now, we assume that the speed be to get the emf

Then,  

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 5.69 m/s.

wavelength divides in half and speed stays the same.