Home
Class 12
PHYSICS
A point charge q(0) is moved slowly from...

A point charge `q_(0)` is moved slowly from the centre of a ring R, ( that is carrying a charge q) to a distance x from its centre along its axis. What is the work done by the external agent in this process ?
Strategy `:` According to work energy theorem, if there is no change in kinetic energy, we have
`W_(ext)+ W_(E ) = 0`
`implies W _(ext) = - W_(E )`
`= - q_(0)(V_(A)-V_(B))`

Text Solution

Verified by Experts

Potential at point B due to a small element dq is given by
`dV_(B ) = ( dq)/( 4pi epsilon_(0)sqrt(R^(2)+x^(2)))`

`implies V_(a) = int dV_(B) = int (dq)/(4pi epsilon_(0) sqrt(R^(2)+x^(2)))`
` implies V_(B) = (q)/( 4pi epsilon_(0) sqrt(x^(2)+ R^(2)))` ....(i)
In order to calculate potential at point A, subsitute `x=0` in the expression given at equation (i),
`V_(A)= (q)/( 4pi epsilon_(0)R)`
Now `W_(ext) = q_(0)(V_(B) -V_(A))= (q_(0)q)/(4pi epsilon_(0))[(1)/(sqrt(R^(2)+x^(2)))- (1)/(R)]`
Promotional Banner

Topper's Solved these Questions

  • ELECTROSTATIC POTENTIAL AND CAPACITANCE

    AAKASH INSTITUTE|Exercise TRY YOURSELF|110 Videos

  • ELECTROSTATIC POTENTIAL AND CAPACITANCE

    AAKASH INSTITUTE|Exercise ASSIGNMENT (SECTION-A) Objective Type Questions (Only one answer)|47 Videos

  • ELECTROMAGNETIC WAVES

    AAKASH INSTITUTE|Exercise ASSIGNMENT SECTION - D Assertion-Reason Type Questions|25 Videos

  • GRAVITATION

    AAKASH INSTITUTE|Exercise ASSIGNMENT SECTION - D (ASSERTION-REASON TYPE QUESTIONS)|16 Videos

Similar Questions

Explore conceptually related problems

If charge q is induced on outer surface of sphere of radius R, then intensity at a point P at a distance S from its centre is

A point charge q is brought slowly from infinity and is placed at the centre of a conducting neutral spherical shell of inner radius a and outer radius b, then find work done by external agent :

" A charge "q_(0)" is brought from infinity to the centre of a dipole.The work done is "

A capacitor of capacitance 5muF is charged with 5muC charge its capacitance is changed to 2muF by some external agent. The work done by external agent is

Potential on the axis of ring of radius 3R and at distance 4R from centre of ring is (charge on the ring is Q )

A point charge q of mass m is located at the centre of a ring having radius R and charge Q. When it is displaced slightly, the point charge accelerates along the x-axis to infinity, the ultimate speed of the point charge :-

A point charge q is located at the centre of a ring having radius R and charge Q .when it is displaced slightly,the point charge accelerated along x -axis to infinity,the ultimate speed of the point charge (consider no loss in radiation)