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 4.2 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?

Answer 1

5.69 m/s.

Step-by-step 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.

.

`E_(1) = BvL = 0.65 T * 4,2 m/s * L\\=2.73L`

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 * v_(2) * L = 0.65 T * 4.2 m/s * L v_(2) = 5.69 m/s`

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.