Two point charges qA = 3 µC and qB = −3 µC are located 20 cm apart in vacuum.What is the electric field at the midpoint O of the line AB joining the two charges? If a negative test charge of magnitude 1.5 × 10−9 C is placed at this point, what is the force experienced by the test charge?

Question 1.8: Two point charges q_A = 3 µC and q_B = −3 µC are located 20 cm apart in vacuum.What is the electric field at the midpoint O of the line AB joining the two charges? If a negative test charge of magnitude 1.5 × 10⁻⁹ C is placed at this point, what is the force experienced by the test charge?

Answer:

Method - 1 

The situation is represented in the given figure. O is the mid-point of line AB.

Distance between the two charges, AB = 20 cm ∴AO = OB = 10 cm

Net electric field at point O = E

Electric field at point O caused by +3µC charge,

E₁ =      along OB

Where,

= Permittivity of free space

Magnitude of electric field at point O caused by −3µC charge,

E₂ =      =          along OB

 = 5.4 × 10⁶ N/C along OB

Therefore, the electric field at mid-point O is 5.4 × 10⁶ N C⁻¹ along OB.

(b) A test charge of amount 1.5 × 10⁻⁹ C is placed at mid-point O. q = 1.5 × 10⁻⁹ C

Force experienced by the test charge = F

∴F = qE

= 1.5 × 10⁻⁹ × 5.4 × 10⁶ = 8.1 × 10⁻³ N

The force is directed along line OA. This is because the negative test charge is repelled by the charge placed at point B but attracted towards point A. Therefore, the force experienced by the test charge is 8.1 × 10⁻³ N along OA.

Method - 2