Question

Two similar spheres when placed 2 cm apart attract each other with a
force of 4 dynes. The spheres are connected by a wire. On removing
the wire the spheres now repel each other with a force of 2.25 dynes.
Calculate the initial charges on the sphere neglecting the capacity of
the wire.​

Answer 1

Answer:

Explanation:

Given :

The distance between two similar sphere charges = d = 2 cm

The force of attraction between charges = - 4 Dynes = - 0.026 N

The force of attraction = + 2.25 Dynes = + 0.015 N

To Find :

The initial charges on the sphere

Solution :

From electrostatic force of attraction

Force between charges  

Force =  

 - 0.026      =                      ..........1

Again

Let a charge of  on wire

So,  Due to this charge , force of repel =  + 0.015 =  

Or,    = 0.015 × 0.0004

i.e   = 0.000006

or,      = 2.58 ×      Column

Again

∵    

So,    =  5.16 ×      Column                ...........2

From eq 1

= - 0.0000104

Or,      = - 1.15 ×                  ..........3

Put the value of   from eq 3 into eq 2

=  5.16 ×      

or,   - 1.15 ×  - 5.16 ×     = 0

Solving this quadratic equation

 = 6.84 ×   C  , - 1.68 ×   C

Now put the value of  in eq 2

 =  5.16 ×  

i.e     = 5.16 ×  - 6.84 ×              and     = 5.16 ×  + 1.68 ×    

or,      = - 1.68 ×  C    and      = 6.84 ×   C

Hence, The initial charges on spheres are 6.84 ×   C  , - 1.68 ×   C and  - 1.68 ×  C , 6.84 ×   C    Answer