Question 125: Electrostats & Capacitance

Question

A charge of 0.8 C is divided into two charges Q$$_1$$ and Q$$_2$$. These are kept at a separation of 30 cm. The force on Q$$_1$$ is maximum when

Accepted Answer

Given, $$Q_1+Q_2=0.8$$ C
$$r=30$$ cm = 0.3 m
$$	herefore$$ According to Coulomb's law
$$F = k{{{Q_1}{Q_2}} \over {{r^2}}}$$
$$ \Rightarrow F = k{{{Q_1}(0.8 - {Q_1})} \over {{r^2}}}$$
The force on Q$$_1$$ will be maximum if
$${{dF} \over {d{Q_1}}} = 0$$
$$ \Rightarrow {d \over {dQ}}k{{{Q_1}(0.8 - {Q_1})} \over {{r^2}}} = 0$$
$$0.8 - 2{Q_1} = 0$$
$$ \Rightarrow {Q_1} = 0.4$$ C
$$	herefore$$ $${Q_2} = 0.8 - {Q_1}$$
$$ = 0.8 - 0.4 = 0.4$$ C

Answer

$$Q_1=Q_2=0.4$$ C

Answer

$$Q_1 \approx 0.8$$ C, $$Q_2$$ negligible

Answer

$$Q_1$$ negligible, $$Q_2 \approx 0.8$$ C

Answer

$$Q_1=0.2$$ C, $$Q_2=0.6$$ C

Electrostats & Capacitance

A charge of 0.8 C is divided into two charges Q$_1 and Q_2. These are kept at a separation of 30 cm. The force on Q_1$ is maximum when

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