Two point charges qA = 3 µC and qB = −3 µC are located 20 cm apart in vacuum. (a) What is the electric field at the midpoint O of the line AB joining the two charges? (b) 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 8:

Two point charges q_A = 3 µC and q_B = −3 µC are located 20 cm apart in vacuum.

(a)   What is the electric field at the midpoint O of the line AB joining the two charges?

(b)   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?

Solution: 

Two point charges q_A = 3 µC and q_B = −3 µC are located 20 cm apart in vacuum.

(a)   What is the electric field at the midpoint O of the line AB joining the two charges?

   Given that

q_A = 3 µC  = 3 × 10 ^{– 6}  C

q_B = −3 µC  =  - 3 × 10 ^{– 6}  C

Distance AB = 20 cm = 0.2 m

In this problem, O is the mid-point of line AB.

OB = OA = 0.2/2  = 0.1 m

The electric field produced by the charge Q at a point r is given as

Plug the values we get

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

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

The direction of electric field is always positive to negative so that

Direction of electric field will in direction of OB

Total electric field due to both charge

E _total = E₁ + E₂

 

Plug 1/4πε0  = 9 × 10⁹ Nm²C^-2

We get

E _total = 5.4 × 10⁶ N/C along OB

Answer

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

Given that 

(b)   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?

q = 1.5 × 10⁻⁹ C

Force experienced by the test charge = F

Use formula of electrostatic force of attraction

F = qE

Plug the values in this formula we get

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

Here placed charge is negative so negative charge at point B will repel while positive change at point A will attract. Hence the direction of force will along OA

Answer

The force experienced by the test charge = 8.1 × 10⁻³ N along the direction of OA.