WBJEE 2019 Physics Solved Paper

According to the question,Force experienced by the charge −q due to charge Q
F=−‌

2kQq

r2

‌cos‌θ... (i) [ where, .k=‌

1

4πε0

]
Fron diagram, cos‌θ=‌

x

r

By substituting the value of cos‌θ in Eq. (i)
F=−‌

2kQq

r2

⋅‌

x

r

or F=−‌

2kQx

r3

or F=−‌

2kQx

(x2+d2)3/2

  [

∵r2=x2+d2

r=√x2+d2

]
For, x<<d, so x2 can be neglected
F=−‌

2kQx

d3

So, the force developed by negative charge (−q) due to the system of the charges as shown in the figure is.
F=‌

−4kQqx

d3

⇒F∝x
So, the forced developed by negative charge i directly proportional to the distance x.