As shown in figure, two vertical conducting rails separated by distance 1.0 m are placed parallel to z -axis. At z = 0 , a capacitor of 0.15 F is connected between the rails and a metal rod of mass 10

Question

As shown in figure, two vertical conducting rails separated by distance $1.0 m$ are placed parallel to $z$ -axis. At $z = 0$ , a capacitor of $0.15 F$ is connected between the rails and a metal rod of mass $100 gm$ placed across the rails slides down along the rails. If a constant magnetic fields of $2.0 T$ exists perpendicular to the plane of the rails, what is the acceleration of the rod? (Take $g = 9.8 m / s^{2}$ )

TestHub · Accepted Answer

Due to motion of rod, emf induced across capacitor, ε = Bl v ∴ Charge stored in capacitor, Q = C ( Bl v ) I = d t d Q ​ = CBl d t d v ​ = CBl a Force opposing the downward motion, F m ​ = B I l ∴ F m ​ = B ( CBl a ) l = B 2 l 2 C a Net force on rod, F net ​ = W − F m ​ = m g − B 2 l 2 C a ∴ ma = m g − B 2 l 2 C a or a = ( m + B 2 l 2 C ) m g ​ So, a = ( 0.1 + 2 2 × 1 2 × 0.15 ) 0.1 × 9.8 ​ = 1.4 m / s 2

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