For given arrangement, where four charge fixed at ends of as quare as given, find value of additiona

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1. Electric Charges and Fields

hard

For given arrangement, where four charge fixed at ends of as quare as given, find value of additional charge $Q$ to be put on one of the vertices so that component of net electric field along the vertical symmetric axis is zero at every point on the vertical

$-q$

$-3q$

$-5q$

$-4q$

Solution

For zero electric field compment along axis

$\frac{\mathrm{k}(4 \mathrm{q}) \mathrm{h}}{\left(\frac{\mathrm{a}^{2}}{2}+\mathrm{h}^{2}\right)^{3 / 2}}=\frac{\mathrm{K}(\mathrm{Q})}{\left(\frac{\mathrm{a}^{2}}{2}+\mathrm{h}^{2}\right)^{3 / 2}}$

$Q=4 q$

$Q=4 q$ (with, negative sign)

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For given arrangement, where four charge fixed at ends of as quare as given, find value of additional charge $Q$ to be put on one of the vertices so that component of net electric field along the vertical symmetric axis is zero at every point on the vertical

Solution

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A charged oil drop is suspended in a uniform field of $3 \times$ $10^{4} V / m$ so that it neither falls nor rises. The charge on the drop will be $…..\times 10^{-18}\; C$

(take the mass of the charge $=9.9 \times 10^{-15} kg$ and $g=10 m / s ^{2}$ )