Question

Two similar spheres having +Q and -Q charge are kept at a certain distance. F force acts between the two. If in the middle of two spheres, another similar sphere having +Q charge is kept, then it experiences a force in magnitude and direction as

Answer 1

Given:

Two similar spheres having +Q and -Q charge are kept at a certain distance. F force acts between the two. In the middle of two spheres, another similar sphere having +Q charge is kept,

To find:

Direction and magnitude of force experienced by the middle charge.

Calculation:

In the 1st case , the net force is :

$\therefore \: F = \dfrac{k(Q \times Q)}{ {d}^{2} }$

$= > \: F = \dfrac{k {Q}^{2} }{ {d}^{2} }$

In the 2nd case ; the middle charge will experience repulsion from +Q and attraction from -Q charge.

Hence , the net force will be directed towards the negative charge.

$\therefore \: F2 = \dfrac{k {Q}^{2} }{ {( \frac{d}{2}) }^{2} } + \dfrac{k {Q}^{2} }{ {( \frac{d}{2}) }^{2} }$

$= > \: F2 = \dfrac{4k {Q}^{2} }{ {d}^{2} } + \dfrac{4k {Q}^{2} }{ {d}^{2} }$

$= > \: F2 = \dfrac{8k {Q}^{2} }{ {d}^{2} }$

$= > \: F2 =8 \times \dfrac{k {Q}^{2} }{ {d}^{2} }$

$= > \: F2 =8 \times F$

$= > \: F2 =8 F$

So the new force will be 8 times the initial force.