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The capacitor plates are fixed on an inclined plane and connected to a battery of emf E. The capacitor plates have plate area a, length l, and the distance between them is d. A dielectric slab of mass m and dielectric constant K is inserted into the capacitor and tied to mass M by a massless string as shown in the figure. Find the value of M for which the slab will stay in equilibrium. There is no friction between slab and plates.

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$\frac{m}{2} - \frac{E^{2} ε_{0} A (k - 1)}{\lg d}$

$\frac{m}{2} + \frac{E^{2} ε_{0} A (k - 1)}{2 \lg d}$

$\frac{m}{2} - \frac{E^{2} ε_{0} A (k - 1)}{2 \lg d}$

$\frac{m}{2} + \frac{E^{2} ε_{0} A (k - 1)}{\lg d}$

answer is A.

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Detailed Solution

For equilibrium, we have

T = Mg

And $T = F + mgsin 30^{\circ}$

or $Mg = F + \frac{mg}{2}$

or $M = \frac{m}{2} + \frac{F}{g} = \frac{m}{2} + \frac{E^{2} ε_{0} A (k - 1)}{2 \lg d}$

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