Question

An emf of 0.08 V is induced in a metal rod of length 10 cm held normal to a uniform magnetic field of 0.4 T, when moves with a velocity of:

• A. 20 ms^-1
• B. 2 ms^-1
• C. 0.5 ms^-1
• D. 3.2 ms^-1

Answer 1

The Correct Option is B

To solve the problem of finding the velocity at which the metal rod is moved, we can use the formula for electromotive force (emf) induced in a conductor moving through a magnetic field:

E = B \cdot l \cdot v

Where:

• E is the induced emf (in volts),
• B is the magnetic field strength (in teslas),
• l is the length of the rod (in meters),
• v is the velocity of the rod (in meters per second).

Given values:

• E = 0.08 \text{ V}
• B = 0.4 \text{ T}
• l = 10 \text{ cm} = 0.1 \text{ m}

We need to find the velocity v. Rearrange the formula to solve for v:

v = \frac{E}{B \cdot l}

Substituting the given values:

v = \frac{0.08}{0.4 \cdot 0.1}

Calculate the denominator:

0.4 \cdot 0.1 = 0.04

Calculate the velocity:

v = \frac{0.08}{0.04} = 2 \text{ m/s}

Therefore, the correct velocity is 2 ms^-1. This corresponds to the given option:

• 2 ms^-1

Thus, the correct answer is: 2 ms^-1.