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Thread: Non uniform linear charge density?

  1. #1
    Super Member fardeen_gen's Avatar
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    Non uniform linear charge density?

    The plastic rod of length $\displaystyle L$ in the diagram has non uniform linear charge density $\displaystyle \lambda = cx$ where c is a positive constant.

    (a) With V = 0 at infinity, find the electric potential at point $\displaystyle P_2$ on the y-axis, at a distance y from one end of the rod.

    (b) From that result, find the electric field component $\displaystyle E_y$ at $\displaystyle P_2$

    (c) Why cannot the field component $\displaystyle E_x$ at $\displaystyle P_2$ be found using the result of (a)?
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by fardeen_gen View Post
    The plastic rod of length $\displaystyle L$ in the diagram has non uniform linear charge density $\displaystyle \lambda = cx$ where c is a positive constant.

    (a) With V = 0 at infinity, find the electric potential at point $\displaystyle P_2$ on the y-axis, at a distance y from one end of the rod.

    (b) From that result, find the electric field component $\displaystyle E_y$ at $\displaystyle P_2$

    (c) Why cannot the field component $\displaystyle E_x$ at $\displaystyle P_2$ be found using the result of (a)?
    Considering small length $\displaystyle dx$ of the rod, the charge$\displaystyle dq$will be given by $\displaystyle \lambda dx$

    Hence, potential at point $\displaystyle P_2$ will be given by
    $\displaystyle \int_0^L \frac{dq}{4\pi\epsilon_0 r}$

    where 'r' is the distance of the small element from $\displaystyle P_2$

    $\displaystyle E_x$ could not be calculated from expression for potential derived in (a) because it requires the expression to be a function of x whereas in (a) it has been derived as function of y.
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