Question

The electric dipole moment of p vector placed in a uniform electric field of intensity E vector at an angle teta with the respect to the field the direction of torque is

Answer 1

Answer:

an electric dipole moment P is placed in a electric field of intensity E. the dipole acquires a position such that the axis of O with the direction of the field.

Answer 2

Concept:

The cross product of any two vectors is another vector that is perpendicular to both the given two vectors.

Given:

An electric dipole moment with a p vector is placed in a uniform electric field of intensity E vector at an angle theta with respect to the field.

Find:

The direction of torque when the dipole moment is p and an electric field is of intensity E with an angle theta.

Solution:

The electric dipole moment of the p vector is placed in a uniform electric field E such that the axis of the dipole forms an angle θ with the electric field.

The force on the charges on the dipole can be written as

Vector (F+) = +q (vector) E  

Vector (F-) = -q (vector) E

The components of force which are perpendicular to the dipole are

F+ = +qEsinθ  

F- = -qEsinθ  

As the force magnitudes are equal and are separated by a distance d, the torque on the dipole can be written as

Torque (τ) = Force × Distance

τ = (qE) (d) sinθ  

The dipole moment can be given by  

p = qd  

The direction of the dipole moment is from the positive to the negative charge and the direction of the Electric field is also positive.  

Thus, torque can be written as:

τ = pEsinθ

From the above relation, the torque can be written as the cross-product of dipole moment and electric field. So, the direction of the torque will be perpendicular to both.

Hence, the direction of the torque is perpendicular to the dipole moment and electric field both.

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