Question

A particle having a charge 10 mC is held fixed on a horizontal surface. A block of mass 80 g and having charge stays in equilibrium on the surface at a distance of 3 cm from the first charge. The coefficient of friction between the surface and the block is $\mu =0.5$. Find the range within which the charge on the block may lie

• A. $-4\times {10}^{-12}C$ to $4\times {10}^{-12}C$
• B. $-2C$ to $2\times {10}^{2}C$
• C. $-4\times {10}^{-19}C$ to $4\times {10}^{-19}C$
• D. $-2\times {10}^{-19}C$ to $2\times {10}^{-19}C$

Answer 1

Answer: (A)

$-4\times {10}^{-12}C$ to $4\times {10}^{-12}C$

Maximum force that can act due to friction is $mg\mu$ ,which is equal to $0.4N.$

Force due to charge has to be less than $0.4N$.

Now force between the two is

$F=\frac{K{q}_1{q}_2}{r^2}=\frac{9\times {10}^9\times 0.01q_1}{{0.03}^2}<0.4$

Above equation implies charge has to be less than $4\times {10}^{-12}C$, so option 1 is best.