NEET2017PhysicsElectromagnetic InductionActual
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 )
Options
- A2.5 ~m / s ^2
- B1.4 ~m / s ^2
- C9.8 ~m / s ^2
- D0
Correct answer
B. 1.4 ~m / s ^2
Step-by-step solution
Due to motion of rod, emf induced across capacitor, =B l v Charge stored in capacitor, Q=C(B l v)I= d Q d t =C B l d v d t =C B l a Force opposing the downward motion, F_m=B I l F_m=B(C B l 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 m a=m g-B^2 l^2 C a or a= m g (m+B^2 l^2 C ) So, a= 0.1 9.8 (0.1+2^2 1^2 0.15 ) =1.4 ~m / s ^2