Question

A rod of length 2 m slides with a speed of 5 ms^-1 on a rectangular conducting frame as shown in figure. There exists a uniform magnetic field of 0.04 T perpendicular to the plane of the figure. If the resistance of the rod is 3 Ω. The current through the rod is

• A. 75 mA
• B. 133 mA
• C. 0.75 A
• D. 1.33 A

Answer 1

The Correct Option is B

The induced electromotive force (EMF) in the rod is given by the formula: \[ \text{EMF} = B \times v \times l \] Where:
\( B \) is the magnetic field strength (0.04 T),
\( v \) is the velocity of the rod (5 ms\(^{-1}\)),
\( l \) is the length of the rod (2 m).
Substituting the values: \[ \text{EMF} = 0.04 \times 5 \times 2 = 0.4 \, \text{V} \] Now, using Ohm’s Law, the current through the rod is: \[ I = \frac{\text{EMF}}{R} = \frac{0.4}{3} = 0.1333 \, \text{A} = 133 \, \text{mA} \] Thus, the current through the rod is 133 mA.