C
CraftExam
medium difficulty10 min

Electric Dipole, Dipole Field and Torque

An electric dipole is a pair of equal and opposite charges separated by a small distance. Its dipole moment is p = q(2a), directed from negative charge to positive charge.

In one line: Dipole moment points minus to plus; torque tries to turn p toward E.

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Understand it

  • A dipole has no net charge, but it produces an electric field because its positive and negative charges are separated.
  • If charges -q and +q are separated by 2a, the dipole moment p has SI unit C m.
  • The electric field is different on the axial line and equatorial line.
  • On the axial line, field is along the dipole moment direction outside the dipole; on the equatorial line, field is opposite to dipole moment.
  • In a uniform electric field, a dipole experiences torque τ = p × E, which tends to align it with the field.

Example

A dipole with q = 3 microC and separation 4 cm has p = q(2a) = (3 × 10−6)(0.04) = 1.2 × 10−7 C m, directed from -q to +q.

Formula and rule

p = q(2a), SI unit C m.

Axial field for a short dipole: Eaxial = (1/4πε0)(2p/r3).

Equatorial field for a short dipole: Eequatorial = (1/4πε0)(p/r3), opposite to p.

Torque in uniform field: τ = pE sinθ, vector form τ = p × E.

These short-dipole formulae apply when r is much greater than dipole length.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A dipole has q = 5 microC and separation 2 cm.

  1. 1p = (5 × 10−6 C)(0.02 m) = 1.0 × 10−7 C m.
  2. 2If placed in a uniform electric field E = 3 × 105 N C−1 at 30 degrees, torque τ = pE sin30 = (1.0 × 10−7)(3 × 105)(0.5) = 1.5 × 10−2 N m.

Method you can reuse

  1. 1Draw the dipole and mark -q, +q, and 2a.
  2. 2Define p with direction.
  3. 3For field derivation, find distances from both charges, write individual fields, resolve or combine directions, apply short-dipole approximation if stated.
  4. 4For torque, use τ = pE sinθ.

Visual tip

Required diagrams: dipole with -q and +q separated by 2a, dipole moment arrow from -q to +q, axial point on dipole axis, equatorial point on perpendicular bisector, and torque diagram in uniform electric field.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What is the direction of electric dipole moment?

Think first, then show answer
Electric dipole moment is directed from the negative charge to the positive charge. This direction is a convention and must be used consistently in torque and field expressions.

Common wrong answer

Using τ = pE cosθ is wrong for torque; sinθ is used because torque depends on the perpendicular component.

Don't mix this up

Students often take separation as a instead of 2a, or reverse the direction of dipole moment.

Exam tip

In derivations, clearly mark axial point, equatorial point, distances from both charges, and final direction of net field. Direction carries marks in dipole questions.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Commonly asked as derivation of field at axial or equatorial point, numerical on dipole moment or torque, and comparison of axial and equatorial fields.
  1. 1

    Enough for 1 mark

    An electric dipole is a pair of equal and opposite charges separated by a small distance. Its dipole moment is p = q(2a), directed from negative charge to positive charge.

  2. 2

    Add for 2 marks

    Example: A dipole with q = 3 microC and separation 4 cm has p = q(2a) = (3 × 10−6)(0.04) = 1.2 × 10−7 C m, directed from -q to +q.

  3. 3

    Add for 3 marks

    If charges -q and +q are separated by 2a, the dipole moment p has SI unit C m.

Practice

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