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A charge +q is fixed at each of the poin...

A charge `+q` is fixed at each of the points `x=x_0`, `x=3x_0`, `x=5x_0`,…………`x=oo` on the x axis, and a charge `-q` is fixed at each of the points `x=2x_0`, `x=4x_0`, `x=6x_0`, …………`x=oo`. Here `x_0` is a positive constant. Take the electric potential at a point due to a charge Q at a distance r from it to be `Q//(4piepsilon_0r)`.Then, the potential at the origin due to the above system of

A

zero

B

`q/(8piepsilon_(0)x_(0)ln2)`

C

infinite

D

`(qln(2))/(4piepsilon_(0)x_(0))`

Text Solution

Verified by Experts

The correct Answer is:
D
Potental at origin will be given by
`V=q/(4piepsilon_(0))[1/x_(0)-1/(2x_(0))+1/(3x_(0))-1/4x_(0)+…]`
`=q/(4pi epsilon_(0))(1/x_(0))[1-1/2+1/3-1/4+…]`
`=q/(4piepsilon_(0)x_(0))ln(2)`
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Knowledge Check

  • Along the x-axis, three charges q/2,-q and q/2 are placed at x=0,x=a and x=2a respectively. The resultant electric potential at a point P located at a distance r from the charge -q , (rgtgta) is : ( epsilon_(0) is the permittivity of free space)

    A
    `(aq)/(4piepsilon_(0)r^(2))`
    B
    `(qa^(2))/(4piepsilon_(0)r^(3))`
    C
    `(q(a^(2)//4))/(4piepsilon_(0)r^(2))`
    D
    `(q)/(4piepsilon_(0)r^(2))`

  • Three charges -1, +q and +q are situated in x-y plane at points (0, -a)(0,0) and (0, a) respectively. The potential at a point distant r(r gt a) in a direction making an angle theta from y - axis will be

    A
    `(kq)/(r )`
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    `(kq)/(r^(2))(2a cos theta)`
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  • Three charge +q,+q and -q are situated in x-y plane at the point (0,a)(0,0)(0,-a). Then, the electric potential at a point in first quadrant whose position vector makes an angle theta with y axis and at a distance r (r gt gt a) from the origin is

    A
    `(qa cos theta)/(2 pi epsilon_(0)r^(2))`
    B
    `(q)/(4 pi epsilon_(0)r)(1+(2a cos theta)/(r))`
    C
    `(q)/(4 pi epsilon_(0)r)`
    D
    `(q)/(4 pi epsilon_(r))(1-(2a cos theta)/(r))`

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