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 the charge Q is located in the plane that bisects the dipole. Assume that r>>s
Immediately after the dipole is released:
a. What is the magnitude of the force on the dipole?
b. What is the magnitude of the torque on the dipole?

Answer 1

Answer:

a) the magnitude of the force is

F= Q($\frac{kqs}{r^3}$) and where k = 1/4πε₀

F = Qqs/4πε₀r³

b)  the magnitude of the torque on the dipole

τ = Qqs/4πε₀r²

Explanation:

from coulomb's law

E = $\frac{kq}{r^{2} }$

where k = 1/4πε₀

the expression of the electric field due to dipole at a distance r is

E(r) = $\frac{kp}{r^{3} }$ , where p = q × s

E(r) = $\frac{kqs}{r^{3} }$ where r>>s

a) find the magnitude of force due to the dipole

F=QE

F= Q($\frac{kqs}{r^3}$)

where k = 1/4πε₀

F = Qqs/4πε₀r³

b) b) magnitude of the torque(τ) on the dipole is dependent on the perpendicular forces

τ = F sinθ × s

θ = 90°

note: sin90° = 1

τ = F × r

recall  F = Qqs/4πε₀r³

∴ τ = (Qqs/4πε₀r³) × r

τ = Qqs/4πε₀r²

Answer 2

Part A: The expression of the force on the dipole is $F = \dfrac {Qqs}{4 \pi \epsilon_0 r^3}$.

Part B: The expression of the torque on the dipole is $\tau = \dfrac {Qqs}{4\pi\epsilon_0 r^2}$.

How do you calculate the force and torque on the dipole?

Given that 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. Also, r>>s.

Part A

The electric field due to dipole at a distance r is given below.

$E_r = \dfrac {qs}{4\pi \epsilon_0 r^3}$

The magnitude of the force can be given as below.

$F = QE_r$

$F = \dfrac {Qqs}{4 \pi \epsilon_0 r^3}$

Hence the expression of the force on the dipole is $F = \dfrac {Qqs}{4 \pi \epsilon_0 r^3}$.

Part B

The torque on the dipole will dependent on the perpendicular forces on the dipole. The expression of the torque is given below.

$\tau = F \times r \times sin \theta$

For the perpendicular forces, θ = 90°. Hence the torque is given below.

$\tau = F\times r$

$\tau = \dfrac {Qqs}{4 \pi \epsilon_0 r^3} \times r$

$\tau = \dfrac {Qqs}{4\pi\epsilon_0 r^2}$

Hence the expression of the torque on the dipole is $\tau = \dfrac {Qqs}{4\pi\epsilon_0 r^2}$.

To know more about force and torque, follow the link given below.

https://brainly.com/question/18992494.