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NEET-XII-Physics

29: Electric Field and Potential

with Solutions - page 3
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  • #8
    The electric field in a region is directed outward and is proportional to the distance r from the origin. Taking the electric potential at the origin to be zero,
    (a) it is uniform in the region
    (b) it is proportional to r
    (c) it is proportional to r2
    (d) it increases as one moves away from the origin
    digAnsr:   c
    Ans : (c) it is proportional to r2
    Given:
    E`` \propto ``r and V = 0 at r =0
    `` \Rightarrow ``E = kr
    Also, E = `` \frac{-dV}{dr}``
    `` \therefore V=-\int Edr``
    `` \Rightarrow V=-\int krdr``
    `` \Rightarrow V=-k\frac{{r}^{2}}{2}+C``
    Using the condition, V = 0 at r = 0, we get C =0.
    Therefore,
    `` V=-k\frac{{r}^{2}}{2}``
    `` \Rightarrow V\propto {r}^{2}``
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