Home
Class 12
PHYSICS
A rod of length L lies along the x-axis ...

A rod of length L lies along the x-axis with its left end at the origin. It has a non-uniform charge density `lamda=alphax`, where a is a positive constant.
(a) What are the units of `alpha`?
(b) Calculate the electric potential at point A where `x = - d` .

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
a. `alpha=lamda/x=(C//m)/m=C/m^2`
`b.

`dV1/(4piepsilon_0).(dq)/(x+d)`
`=(1/(4piepsilon_0) ((lamdaxdx)/(x+d))`
`=(1/(4piepsilon_0)) ((alphaxdx)/(x+d))`
`:. V=int_(x=0) ^(x=L) dV=alpha/(4piepsilon_0) [L-d("In" (1+L/d)]`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ELECTROSTATICS

    DC PANDEY|Exercise Exercise 24.7|2 Videos

  • ELECTROSTATICS

    DC PANDEY|Exercise Level 1 Assertion And Reason|19 Videos

  • ELECTROSTATICS

    DC PANDEY|Exercise Exercise 24.5|3 Videos

  • ELECTROSTATIC POTENTIAL AND CAPACITORS

    DC PANDEY|Exercise (C) Chapter exercises|50 Videos

  • GRAVITATION

    DC PANDEY|Exercise All Questions|120 Videos

Similar Questions

Explore conceptually related problems

A continuous line of charge of length 3d lies along the x-axis, extending from x + d to x + 4d, The line carries a uniform linear charge density lambd . In terms of d, lambda and any necessary physical constant find the magnitude of the electric field at the origin.

A straight rod of length L has one of its end at the origin and the other at X=L . If the mass per unit length of the rod is given by Ax where A is constant, where is its centre of mass?

Knowledge Check

  • A rod of length 'l' is placed along x-axis. One of its ends is at the origin. The rod has a non-uniform charge density lambda= a, a being a positive constant. Electric potential at P as shown in the figure is -

    A
    `(a)/(4pi epsilon_(0)) ln((b+l)/(b))`
    B
    `(a)/(4pi epsilon_(0)) "ln" (l)/(b)`
    C
    `(a)/(4pi epsilon_(0)) "ln"(b)/(l)`
    D
    zero

  • A rod of length l is placed along x - axis. One of its ends is at the origin. The rod has a non - uniform charge density lambda=(a)/(x) , a being a positive constant. The electric potential at the point P (origin) as shown in the figure is

    A
    `V=(a)/(4pi epsilon_(0))((l)/(b(b+l)))`
    B
    `V=(a)/(4pi epsilon_(0))((b)/(l(b+l)))`
    C
    `V=(a)/(4pi epsilon_(0))((b)/(l))`
    D
    `V=(a)/(4pi epsilon_(0))((l)/(b))`

  • A rod lies along the x-axis with one end at the origin and the other at x rarr oo . It carries a uniform charge lambda C/m. The electric field at the point x = -a on the axis will be

    A
    `vec(E) = (lambda)/(4pi epsilon_(0)a)(-hat(i))`
    B
    `vec(E) = (lambda)/(4pi epsilon_(0)a)(hat(i))`
    C
    `vec(E) = (lambda)/(2pi epsilon_(0)a)(-hat(i))`
    D
    `E = (lambda)/(2pi epsilon_(0)a)(hat(i))`

    • Similar Questions

    Explore conceptually related problems

    A continuous line of charge oflength 3d lies along the x-axis, extending from x + d to x + 4d . the line carries a uniform linear charge density lambda . In terms of d, lambda and any necessary physical constants, find the magnitude of the electric field at the origin:

    A non-uniform thin rod of length L is palced along X-axis so that one of its ends is at the origin. The linear mass density of rod is lambda = lambda_(0)x . The centre of mass of rod divides the length of the rod in the ratio:

    A rod lies along the X-axis with one end at the origin and the other at x rarr oo . It carries a uniform charge lambda Cm^(-1) . The electric field at the point x=-a on the axis will be

    A rod length L and mass M is placed along the x -axis with one end at the origin, as shown in the figure above. The rod has linear mass density lamda=(2M)/(L^(2))x, where x is the distance from the origin. Which of the following gives the x -coordinate of the rod's center of mass?

    A non–uniform thin rod of length L is placed along x-axis as such its one of ends at the origin. The linear mass density of rod is lambda=lambda_(0)x . The distance of centre of mass of rod from the origin is :

    Home
    Profile