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A conducting rod of length 0.40 m slides without friction on two…
Question
A conducting rod of length 0.40 m slides without friction on two parallel horizontal rails connected by a resistor; the total circuit resistance is 2.0 ohm. A uniform magnetic field of 0.50 T is directed vertically (perpendicular to the plane of the rails). The rod is pulled at a constant speed of 10 m/s. Find the external force (in newtons) required to keep the rod moving at this constant speed.
✓ Verified answer: 0.2checked by our engine — not a guess
Step-by-step solution
Motional EMF = B L v = 0.50 x 0.40 x 10 = 2.0 V.
Current I = EMF/R = 2.0/2.0 = 1.0 A.
Magnetic force on rod F = B I L = 0.50 x 1.0 x 0.40 = 0.20 N.
At constant speed the applied force balances this: F = B^2 L^2 v / R = 0.25 x 0.16 x 10 / 2 = 0.20 N.
Final answer0.2
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