Electric Dipole In Uniform Electric Field

Electric Dipole-

 

Before you go through this article, make sure that you have gone through the previous article on Electric Dipole.

 

We have learnt-

• A system of two equal and opposite charges separated by a small distance is called as electric dipole.
• Electric dipole moment of an electric dipole is defined as the product of magnitude of either charge and the dipole length having its direction from -q to +q.

 

Electric Dipole

 

In this article, we will discuss Electric dipole In Uniform Electric Field.

 

Electric Dipole In Uniform Electric Field-

 

Consider-

• An electric dipole consisting of two charges -q and +q separated by a distance of 2ℓ.
• The electric dipole is placed in a uniform electric field.
• The electric dipole moment vector of the electric dipole makes an angle θ with the electric field.

 

This is shown below-

 

 

Force On Electric Dipole In Uniform Electric Field-

 

We know,

• A positive charge always experiences a force in the direction of electric field.
• A negative charge always experiences a force in the direction opposite to electric field.

 

So, Force exerted on charge +q is given by-

 

 

So, Force exerted on charge -q is given by-

 

 

These two forces on the electric dipole may be represented as-

 

 

Now, by superposition principle, the net force on the electric dipole in the uniform electric field is given by- 

 

 

Thus, There is no net force acting on the electric dipole in uniform electric field. So, it does not perform a translational motion.

 

Torque On Electric Dipole In Uniform Electric Field-

 

• The two equal and opposite forces acting on the electric dipole forms a couple.
• This couple tends to rotate the dipole in the electric field by exerting a torque on it.

 

The torque acting due to the couple is given by-

 

 

 

We put-

• Magnitude of Force = qE
• Perpendicular distance between the two forces = 2ℓsinθ

 

Substituting the values, the torque on the electric dipole is calculated as-

 

 

Thus, torque on an electric dipole in a uniform electric field is given by-

 

 

In vector form,

 

 

Thus, An electric dipole experiences a torque in a uniform electric field given by T = pEsinθ. So, it performs a rotatory motion.

 

Special Cases-

 

Case-01: When electric dipole is parallel to the electric field (θ=0°)-

 

 

In this case, the torque experienced by the electric dipole is given by-

T = pEsin0° = 0

Thus, when electric dipole gets aligned with the electric field, the torque becomes zero.

 

In this position, the electric dipole is in stable equilibrium.

 

Case-02: When electric dipole is anti-parallel to the electric field (θ=180°)-

 

 

In this case, the torque experienced by the electric dipole is given by-

T = pEsin180° = 0

Thus, when electric dipole gets aligned in the direction opposite to the electric field, the torque becomes zero.

 

In this position, the electric dipole is in unstable equilibrium.

 

Case-03: When electric dipole is perpendicular to the electric field (θ=90°)-

 

 

In this case, the torque experienced by the electric dipole is given by-

T = pEsin90° = pE (maximum)

Thus, when electric dipole is perpendicular to the electric field, it experiences the maximum torque.

 

In this position, the electric dipole experiences the maximum torque.

 

Electric Dipole In Non-Uniform Electric Field-

 

In non-uniform electric field,

• The +q and -q charges of the electric dipole experience different forces (not equal and opposite). Hence, a net force acts on the electric dipole in non-uniform electric field.
• Also, a net torque acts on the electric dipole which depends on the location of the dipole in the field.

 

Thus, an electric dipole experiences a force as well as a torque in a non-uniform electric field.

 

Read the next article on-

Electric Flux

 

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