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Electric Dipole z Electric dipole – two equal magnitude, opposite charged particles separated by distance d z What’s the electric field at point P due to the dipole? Electric Dipole z Approximate E field for a dipole is 2 kqd E = 3 z z Define electric dipole moment, p as, r r p=qd z The direction of p and d is from the negative to positive z E field along dipole axis at large distances (z>>d) is 2kp E= 3 z Electric Dipole in an E-field z What happens when a dipole is put in an electric field? (com = center of mass) z Net force, from uniform E, is zero z But force on charged ends produces a net torque about its center of mass Torque on an Electric Dipole z Definition of torque z For dipole rewrite it as τ = r × F = rF sin φ τ = xF sin θ + (d − x)F sin θ = d F sin θ = (qd)(F/q) sin θ Thus: τ = p × E Torque on an Electric Dipole z z z Torque acting on a dipole tends to rotate p into the direction of E Associate potential energy, U, with the orientation of an electric dipole in an E field Dipole has least U when p is lined up with E Energy Stored in an Electric Dipole z z Remember θ θ 90 90 U = −W = − ∫ τ d θ = ∫ pE sin θ d θ Potential energy of a dipole U = − pE cos θ = −p • E z U is least (greatest) when p and E are in same (opposite) directions Exercise z Rank a) magnitude of torque and b) U , greatest to least τ = p × E = pE sin θ z a) Magnitudes are same U = −p • E = − pE cosθ z U greatest at θ=180 z b) 1 & 3 tie, then 2 &4