Question

Two positive charges each of charge q are kept at (a, 0) and (-a, 0). A negative charge is left from position (0, a) then negative charge will perform

Oscillatory motion

Simple harmonic motion

Will come to rest at centre

Will continue moving along negative y-axis​

Answer 1

Given:

Two positive charges each of charge q are kept at (a, 0) and (-a, 0). A negative charge is left from position (0, a).

To find:

Type of motion followed by the negative charge?

Calculation:

Force on the charge (-Q) : (REFER TO DIAGRAM)

$F = 2f_{e} \cos( \theta)$

• f_(e) is Electrostatic Force
• $\sin(\theta)$ component of force will be cancelled.

$\implies F = 2 \times \dfrac{kQq}{{(a \sqrt{2})}^{2} } \times \dfrac{a}{a \sqrt{2} }$

$\implies F = 2 \times \dfrac{kQq}{2 {a}^{2} } \times \dfrac{1}{\sqrt{2} }$

$\implies F = \dfrac{kQq}{ {a}^{2} \sqrt{2} }$

Now, this force is pulling in nature (i.e. attractive). So,

• on +Y axis, negative charge will experience force towards -Y axis.

• Vice versa.

-Q will follow Oscillatory Motion (OPTION 1)