Question

If two identical spheres having charge 16C and -8 C are kept at certain distance apart, then the force is F. They are touched and again kept at the same distance, the force becomes......?????

Answer 1

When two identical spheres having charges Q 1 and Q 2 are kept distance d apart from each other an electrostatic  force of attraction F is produced between them

$\longrightarrow\mathtt{ F = \dfrac{ K Q_1Q_2}{d^{2} }}$

here ,

• K = proportionality constant = 8.99 x 10 ⁹ Nm² /C ²

• Q 1 = 16 C

• Q 2 = - 8 C

• d = distance between the two charges

Now let's substitute the values in the above equation ,

$\longrightarrow\mathtt{ F = \dfrac{ K\times 16 \times (-8)}{d^{2} }}...(1)$

Now both the charges are touched and are again kept at the same distance

Charges on both the spheres will be ,

$\longrightarrow\mathtt{ Q =\dfrac{ Q_1 + Q_2}{2} }$

$\longrightarrow\mathtt{ Q =\dfrac{ 16-8 }{2} }$

$\longrightarrow\mathtt{ Q =\dfrac{ 8}{2} }$

$\longrightarrow\mathtt{ Q =4 C }$

Charge on each sphere = 4 C

Similarly ,

$\longrightarrow\mathtt{ F ' = \dfrac{ K QQ}{d^{2} }}$

$\longrightarrow\mathtt{ F' = \dfrac{ K 16 }{d^{2} }}...(2)$

By comparing equation( 1 )and (2 )we can say that ,

$\longrightarrow\mathtt{ F = - 8 F' }$

$\longrightarrow\boxed{\mathtt{ F' = \dfrac{-F}{8}}}$