A small charged sphere of mass m is suspended with a string in a uniform field $E = (A ¯ i + B ¯ j)$ Where A and B are positive constants. The sphere is in equilibrium at an angle $θ$ with the vertical. The charge on the ball is

\frac{m g s i n θ}{A + B s i n θ}

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\frac{m g c o s θ}{A + B c o s θ}

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\frac{m g t a n θ}{A + B t a n θ}

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\frac{m g A}{m a + B t a n θ}

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Solution

The correct option is C $\frac{m g t a n θ}{A + B t a n θ}$
As we know, $¯ F = q ¯ E$
$¯ F = q (A ¯ i + B ¯ j) T c o s θ + B q = m g T s i n θ = A q$
So, $q = \frac{m g t a n θ}{A + B t a n θ}$

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