(a) Calculate the net electric force acting on the dipole....

(a) Calculate the net electric force acting on the dipole.
(b) Show that the magnitude of the torque on the dipole is $\tau=q E d \sin \theta .$ (c) Calculate the torque acting on the dipole for $\theta=0,36.9^{\circ},$ and $90.0^{\circ} .$

Key Concepts

Superposition Principle in Electrostatics

This principle states that the total force on a charge or system of charges is the vector sum of the individual forces exerted by each contributing charge or electric field component. It is used to calculate the net force acting on each charge of a dipole, leading to the overall net force and torque on the dipole.

Torque on an Electric Dipole

When an electric dipole is placed in an electric field, it experiences a torque that tends to align the dipole moment with the field. The magnitude of this torque is given by ? = pE sin ?, where p is the dipole moment, E is the electric field strength, and ? is the angle between the dipole moment and the field direction.

Electric Dipole Moment

The electric dipole moment is a vector quantity defined as the product of the magnitude of one of the charges and the separation distance between the charges. It represents the strength and orientation of the dipole and is typically directed from the negative charge to the positive charge.

Net Force on an Electric Dipole

In a uniform electric field, the forces acting on the positive and negative charges of a dipole are equal in magnitude but opposite in direction, resulting in a net force of zero. However, in a nonuniform electric field, the difference in field strength across the dipole results in a net force, which is determined by the spatial variation (gradient) of the electric field.

Transcript

0:00 Hi.

00:02 In the given problem, this is the uniform electric field in the horizontal direction.

00:12 And in this field, a dipole has been kept.

00:17 Suppose this is minus q charge and this is here plus q charge.

00:27 The length of the dipole is given as d.

00:31 These charges, the dipole charges, are having a magnitude plus minus q is equal to plus minus 3 .0 microculum.

00:46 The dipole length d is given as 7 .0 centimeter and this uniform electric field e is having a magnitude of 2 .0 into 10 ratio power 4 newton per coulum.

01:02 Now in the first part of the problem we have to find net force acting on this dipole.

01:08 So here this negative charge will experience an electrostatic force in a direction opposite to the electric field whose magnitude is q into e and this positive charge will experience the same electrostatic force q into e but in the direction of electric field because we know electric field moves from positive to negative so this negative charge will experience a force towards the positive and this positive charge will experience the same force towards the negative.

01:38 Hence the net force experienced by the dipole is let it be f.

01:52 So this will be qe minus qe because the two forces are equal in magnitude and opposite in direction.

02:00 So the net force experienced by the dipole is zero.

02:04 The answer for the first part of the problem...

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