Question

A technician is working on an MRI machine. To test it, the technician turns on the MRI machine that produces a strong magnetic field, but then he accidentally drops a screwdriver in this magnetic field. As the screwdriver falls, an emf is induced across the length of the metal shaft, L, of the screwdriver. At one instant, the screwdriver falls with a speed of 2.1 m/s and is oriented as shown in figure so that the induced emf is maximized. The magnitude of the magnetic field at this instant is 2.5 T, and the length of the metal shaft, L, is 10 cm. What is the induced emf across the length of the metal shank at this instant?

Answer 1

The induced emf across the length of the metal shank at this instant is 0.525 V.

Step-by-step explanation:

The induced emf across the length of the metal shank can be calculated using the formula:

emf = B * v * L

Where: B is the magnetic field strength, v is the velocity of the screwdriver, and L is the length of the metal shank.

Substituting the given values into the formula, we have:

emf = 2.5 T * 2.1 m/s * 0.10 m

Simplifying the equation, the induced emf across the length of the metal shank at this instant is 0.525 V.

Answer 2

0.525 V

Step-by-step explanation:

Noting the given data in the question:

we have,

The speed of the fall of the screw driver, v = 2.1 m/s

The magnitude of the magnetic field, B = 2.5 T

The length of the metal shaft of the screw driver, L = 10 cm = 0.1 m

Now, the induce emf (E) is given as:

E = B × L × v

on substituting the values in the above equation, we get

E = 2.5 × 0.1 × 2.1

or

E = 0.525 V

Hence, the emf induced across the length of the metal shank will be 0.525 V