Most Important Selected Qs for JEE AdvancedPhysicsCapacitance
A parallel plates capacitor is made of square conducting plates of side a and the separation between plates is d. The capacitor is connected with battery of emf V volt as shown in the figure. There is a dielectric slab of dimension a a d with dielectric constant k . At t=0 , dielectric slab is given velocity v₀ towards capacitor as shown in the figure. (Neglect the effect of gravity and electrostatic force acting on
Options
- AMotion of dielectric slab is periodic but not simple harmonic motion
- BMotion of dielectric slab is simple harmonic motion
- CAt any time, the slope of graph of total energy verses x is twice the slope of graph of potential energy verse
- DThe value of maximum energy stored in the system is 1 2 mv ₀^2+ ₀ a ^2 ~V ^2 2 ~d (2 k -1)
Correct answer
D. The value of maximum energy stored in the system is 1 2 mv ₀^2+ ₀ a ^2 ~V ^2 2 ~d (2 k -1)
Step-by-step solution
aligned & C= ₀(a-x) a d + ₀ x a k d & = ₀ a[a-x+k x] d & = ₀ a d [a+(k-1) x] aligned aligned & U = ₀ a ~V ^2 2 ~d [ a +( k -1) x ] & F = dU dx = ₀ aV ^2( k -1) 2 ~d & v ^2= v ₀^2+2 Ax = v ₀^2+ ₀ aV ^2( k -1) md x aligned E= 1 2 m v₀^2+ ₀ a^2(k-1) x 2 d + ₀ a V^2 2 d [a+(k-1) x] E _ = 1 2 mv ₀^2+ ₀ a ^2 ~V ^2(2 k -1) 2 ~d