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    Question

    A rod PQ of length 0.6 m moves on smooth rails with

    speed 3 m/s in a magnetic field B = 0.5 T. The rails form a closed circuit with 4 Ω resistance. Find power dissipated in the resistor.
    A 0.4058 W Correct Answer Incorrect Answer
    B 0.675 W Correct Answer Incorrect Answer
    C 0.576 W Correct Answer Incorrect Answer
    D 0.2025 W Correct Answer Incorrect Answer

    Solution

    Length of rod PQ: L = 0.6 m Speed of rod: v = 3 m/s Magnetic field: B = 0.5 T Circuit resistance: R = 4 Ω Find the induced EMF When a conductor moves through a magnetic field, the motional EMF is: ε = BLv ε = (0.5)(0.6)(3) ε = 0.9 V Step 2: Find the induced current Using Ohm's law: I = ε/R = 0.9/4 = 0.225 A Find the power dissipated Power can be calculated using any of these equivalent formulas: P = I²R P = ε²/R P = εI Using P = I²R: P = (0.225)² × 4 P = 0.050625 × 4 P = 0.2025 W

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