Question

A point charge q is held at a distance r from the center of a dipole that consists of two charges ±q separated by a distance s. The dipole is initially oriented so that q is in the plane bisecting the dipole. Assume that r≫s.

Answer 1

Answer:

Complete question: A point charge Q is held at a distance r from the center of a dipole that consists of two charges ±qseparated by a distance s. The dipole is initially oriented so that the charge Q is located in the plane that bisects the dipole. Assume that r≫s. Immediately after the dipole is released,

what is the magnitude of the force on the dipole?

In the space provided, enter the factor that multiplies 1ϵ0 in your answer. Express this factor in terms of q, Q, s, π, and r.

what is the magnitude of the torque on the dipole?

in the space provided, enter the factor that multiplies 1ϵ0 in your answer. Express this factor in terms of q, Q, s, π, and r.

Answer: The magnitude of he electric field of the dipole = E = Kqs/r³

the magnitude of the torque on the dipole is Z = (qs) (KQ/r²) = 1/ϵ₀ (qQs)/4πr³)

Explanation:

From the given question,

We find the magnitude of the force on the dipole.

E=  the electric field

ϵ₀=  permittivity of free space is  

q = magnitude of each charge of the dipole

The dipole movement =  p =qs

The electric field of the dipole = E = Kqs/r³

Then

F=QE ⇒ F = Q (Kqs)/r³  ⇒ KqQs/r³

= 1/ϵ

₀ ( qQs)/4πr³)

The electric field due to Q is   E = KQ/r²

The next step is to find  the magnitude of the torque on the dipole

The torque is denoted by Z =PE sign 90

Z = (qs) (KQ/r²) = 1/ϵ

₀ (qQs)/4πr³)