Question

The force between 2 indentical
changes separated by 1 cm is
equal to 90 N . What is
the
magnitude of two charges? ​

Answer 1

The force acting between two charges $\sf{q_1}$ and $\sf{q_2}$ separated by a distance $\sf{r}$ is,

$\longrightarrow\sf{F=\dfrac{kq_1q_2}{r^2}\quad\quad\dots(1)}$

where $\sf{k=9\times10^{9}\ N\,m^2\,C^{-2}.}$

According to the question,

• $\sf{q_1=q_2=q\quad\!(Say)}$

• $\sf{r=1\ cm=10^{-2}\ m}$

• $\sf{F=90\ N}$

Hence (1) becomes,

$\longrightarrow\sf{90=\dfrac{9\times10^9\,q^2}{(10^{-2})^2}}$

$\longrightarrow\sf{90=\dfrac{9\times10^9\,q^2}{10^{-4}}}$

$\longrightarrow\sf{90=9\times10^{13}\,q^2}$

$\longrightarrow\sf{q^2=\dfrac{90}{9\times10^{13}}}$

$\longrightarrow\sf{q^2=10^{-12}\ C^2}$

$\longrightarrow\underline{\underline{\sf{|q|=10^{-6}\ C}}}$

Hence the magnitude of the two charges is $\bf{10^{-6}\ C}$ each.