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# The capacitor plates are fixed on inclined plane p connected to a battery of emf E. A dielectric slab of mass m and dielectric constant k is inserted into the capacitor and tied to mass M using a weightless string as shown. If capacitance have plate area A, length l and distance d between them. Find M such that slab stays in equilibrium. Assume zero friction between slab and plates

$(A)\;\frac{m}{2} -\frac{E^2 \in _0 A(k-1)}{2 l gd } \\ (B)\;\frac{m}{2} +\frac{E^2 \in _0 A(k-1)}{ l gd } \\ (C)\; \frac{m}{2} +\frac{E^2 \in _0 A(k-1)}{2 l gd } \\ (D)\;none$

For equilibrium,
$T=mg$
$T= F+mg \sin 30^{\circ}$
=>$Mg=F+ \large\frac{mg}{2}$
=>$M=\large\frac{F}{g}+\frac{m}{2}$
$M= \large\frac{m}{2} +\frac{E^2 \in _0 A(k-1)}{ l gd }$
Hence B is the correct answer.