Derive an expression for the maximum torque acting on an electric dipole, when held in a uniform electric field.

Solution

Consider an electric dipole consisting of charges -q and +q and of length 2a placed in uniform electric field $\overset{⇀}{E}$ makng an angle $θ$ with the direction of electric field.

Force acting on charge -q at A= $- q \overset{⇀}{E}$ (opposite to $\overset{⇀}{E}$ )

Force acting on charge +q at B= $q \overset{⇀}{E}$ (along $\overset{⇀}{E}$ )
Thus, electric dipole is under the action of two equal and unlike parallel forces giving rise to a torque on the dipole.
The magnitude of the torque is given by

$τ = either force \times perpendicular distance between the two forces = qE (AN) = q E (2 a \sin θ) = q (2 a) E sinθ = p E sinθ$

Torque experience maximum dipole when it placed perpendicular to the dirction of Electric field i.e,

$when θ = 90 °$

and $\sin 90 ° = 1$

$∴ τ_{\max} = p E$

Torque aligns the dipole along the direction of the electric field.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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Electric Charges And Fields

Derive an expression for the maximum torque acting on an electric dipole, when held in a uniform electric field.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Electric Charges And Fields

Derive an expression for the maximum torque acting on an electric dipole, when held in a uniform electric field.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?