Home
Class 12
PHYSICS
A positive charge Q is uniformly distrib...

A positive charge Q is uniformly distributed throughout the volume of a dielectric sphere of radius R. A point mass having charge +q and mass m is fired toward the center of the sphere with velocity v from a point at distance `r (r gt R)` from the center of the sphere. Find the minimum velocity v so that it can penetrate `(R//2)` distance of the sphere. Neglect any resistance other than electric interaction. Charge on the small mass remains constant throughout the motion.

Text Solution

Verified by Experts

`(1)/(2)mv^(2)+(Qq)/(4piepsilon_(0))*(1)/(r )=(Qq)/(4pi_(0))[(3R^(2)-(R//2)^(2))/(2R^(3))]=(Qq)/(4pi)[(11R^(2))/(8R^(3))]=(11Qq)/(32piepsilon_(0)R)`
`v^(2)=(2)/(m)[(11Qq)/(32piepsilon_(0)R)-(Qq)/(4piepsilon_(0))*(1)/(r )]`
`rArr v=sqrt((11Qq)/(16piepsilon_(0)Rm)-(Qq)/(2piepsilon_(0))(1)/(mr))`
Promotional Banner

Topper's Solved these Questions

  • ELECTROSTANTICS

    FIITJEE|Exercise MATRIX MATCH TYPE|1 Videos

  • FLUID MECHANICS

    FIITJEE|Exercise ASSIGHNMENT COMPREHENSION NUMERICAL BASED QUESTIONS|2 Videos

Similar Questions

Explore conceptually related problems

A conducting sphere of radius R is charged to a potential of V volts. Then the electric field at a distance r ( gt R) from the centre of the sphere would be

A charge q is uniformly distributed over the volume of a shpere of radius R . Assuming the permittively to be equal to unity throughout, find the potential (a) at the centre of the sphere, (b) inside the sphere as a function of the distance r from its centre.

A solid conducting sphere of radius r is having a charge of Q and point charge q is a distance d from the centre of sphere as shown. The electric potential at the centre of the solid sphere is :

Metallic sphere of radius R is charged to potential V. Then charge q is proportional to

A charge Q is uniformly distributed inside a non- conducting sphere of radius R . Find the electric potential energy stored in the system.

A bullet of mass m and charge q is fired towards a solid uniformly charge sphere of radius R and total charge +q. If it strikes the surface of sphere with speed u, find the minimum value of u so that it can penetrate through the sphere. (Neglect all resistance force or friction acting on bullet except electrostatic forces)

A bullet of mass m and charge q is fired towards a solid unifromly charged sphere of redius R and total cbharge + q . If it strikes the surface of sphere with speed u , find the minimum speeed u so that it can penetrate through the sphere , (Neglect all resistance forces or friction acting on bullet except electrositatic forces ) .

There is a cubical cavity inside a conducting sphere of radius R. A positive point charge Q is placed at the centre of the cube and another positive charge q is placed at a distance 1(gtR) from the centre of the sphere. The sphere is earthed Net charge on the outer surface of conducting sphere is

The electric intensity of outside a charged sphere of radius R at a distance r (r gt R) is