Question

A metallic rod of length 4 m is rotating about perpendicular bisector of the rod with angular velocity of 2 rad/s in presence of transverse magnetic field of 0.5 T. Potential difference developed across ends of rod is

• A. 16 V
• B. 8 V
• C. 0 V
• D. 32 V

Answer 1

The Correct Option is C

The problem at hand involves the calculation of the potential difference generated across the ends of a metallic rod rotating in a magnetic field.

Firstly, let's understand the concept involved:

When a conductive rod rotates in a magnetic field, an electromotive force (emf) is induced across its ends due to electromagnetic induction. This can be calculated using the formula:

EMF = B \cdot \omega \cdot l^2 / 8

where:

• B is the magnetic field strength in Tesla.
• \omega is the angular velocity in radians per second.
• l is the length of the rod in meters.

Let's substitute the values given in the problem:

• B = 0.5 \, \text{T}
• \omega = 2 \, \text{rad/s}
• l = 4 \, \text{m}

Therefore, the potential difference (emf) can be calculated as:

EMF = \frac{0.5 \cdot 2 \cdot 4^2}{8}

EMF = \frac{0.5 \cdot 2 \cdot 16}{8}

EMF = 2 \, \text{V}

However, on close inspection, it appears there is a misunderstanding. As we are calculating the potential difference across the ends of the rod when it is rotating about its perpendicular bisector:

Since the rod rotates about its perpendicular bisector, the effective length l_{\text{eff}} for the potential difference calculation is zero (due to symmetry about the axis of rotation), hence:

EMF = 0

This implies there is no net induced emf across the entire rod, which reaffirms that the potential difference developed across the ends of the rod is indeed 0 \, \text{V}.

Thus, the correct answer is:

• 0 V