Question

46. A charged particle is at a distance r from an infinite
conducting plane maintained at zero potential. When
released from rest, the particle reaches a speed u at a
distance r/2 from the plane. At what distance from the
plane will the particle reach the speed 2u?
(a) r/6
(b) r/3
(c) r/4
(d) r/5​

Answer 1

Answer:

a ur answer plz see to it

Answer 2

Answer:

When the charge q is at a distance x from the plate,the force on it due to conducting plate is given by:-

md²x/dt²=-q²/(4πe0(2x)²)

or,mvdv/dx=-q²/(4πe0(2x)²),where v is the velocity attained by the charge.

On integrating the above eqn. we get,

8pie0mv²/q=1/x+c,where c is integrational constant...(1)

For x=d,v=0

So from (1) we get,

c=-1/d

So,8pie0mv²/q²=(1/x-1/d)....(2)

Given at x=d/2,v=u.

So,

So,8pie0mu²/q²=(2/d-1/d)=1/d

or,u²=q²/(8dπe0m)...(3)

Hence,for v=2u;

8πe0m(4u²)/q²=1/x-1/d

or,x=1/(1/d+8πe0m(4u²)/q²)

or,x=1/(1/d+4u²/u²d) [From (3)]

or,x=d/5

Put r in place of d and you get the correct option as (d) i.e.r/5

NOTE:-e0 used in place of epsilon not(permittivity of free space)