Electric Dipole, Dipole Field and Torque

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

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.

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

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.

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. p = q(2a), SI unit C m. Axial field for a short dipole: E_axial = (1/4πε0)(2p/r^3). Equatorial field for a short dipole: E_equatorial = (1/4πε0)(p/r^3), opposite to p. Torque in uniform field: τ = pE sinθ, vector form τ = p x E. These short-dipole formulae apply when r is much greater than dipole length. A dipole with q = 3 microC and separation 4 cm has p = q(2a) = (3 x 10^-6)(0.04) = 1.2 x 10^-7 C m, directed from -q to +q.

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 x E, which tends to align it with the field. p = q(2a), SI unit C m. Axial field for a short dipole: E_axial = (1/4πε0)(2p/r^3). Equatorial field for a short dipole: E_equatorial = (1/4πε0)(p/r^3), opposite to p. Torque in uniform field: τ = pE sinθ, vector form τ = p x E. These short-dipole formulae apply when r is much greater than dipole length. A dipole has q = 5 microC and separation 2 cm. p = (5 x 10^-6 C)(0.02 m) = 1.0 x 10^-7 C m. If placed in a uniform electric field E = 3 x 10^5 N C^-1 at 30 degrees, torque τ = pE sin30 = (1.0 x 10^-7)(3 x 10^5)(0.5) = 1.5 x 10^-2 N m. Commonly asked as derivation of field at axial or equatorial point, numerical on dipole moment or torque, and comparison of axial and equatorial fields. Using τ = pE cosθ is wrong for torque; sinθ is used because torque depends on the perpendicular component.