Question

If the coulombian force acting between two protons separated by a distance r is F, what would be the force acting between two $\alpha -$particles separated by a distance 2r ?

• A. $\frac{F}{2}$
• B. $F$
• C. $2F$
• D. $3F$

Answer 1

Answer: (B)

$F$

Let the charge of proton is q
Charge of $\alpha -$particle
$=2\times chargeofproton$
$=2q$

The force acting between two protons separated by a distance r is
$F=k\frac{q\cdot q}{r^2}=k\frac{q^2}{r^2}$

The force acting between two $\alpha -$ patricles separated by a distance 2r is
$F^{\prime }=k\frac{2q\cdot 2q}{(2r{)}^2}$
$=k\frac{4q^2}{4r^2}$
or $=k\frac{r^2}{r^2}$
$\Rightarrow F^{\prime }=F$