Solve the following :


Consider the situation shown in figure. Suppose a small electric field Eexists in the space in the vertically upward direction and the upper block carries a positive charge $Q$ on its top surface. The friction coefficient between the two blocks is $g$ but the floor is smooth. What maximum horizontal force Fcan be applied without disturbing the equilibrium?

[Hint: The force on a charge $Q$ by the electric field $E$ is $F=Q E$ in the direction of $E$.]


For block $\mathrm{m}$,

$\mathrm{QE}+\mathrm{N}=\mathrm{mg}$ (vertical equilibrium)


$f f=\mu N=\mu(m g-Q E)$

$\mathrm{F}=\mathrm{T}+\mathrm{ff}$ (Horizontal equilibrium) -(i)

For block M,

T=ff (Horizontal Equilibrium) -(ii)

Solving (i)and(ii),

$F=f f+f t$

$F=2 f f=2 \mu(m g-Q E)$

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