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
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Approximate E field for a dipole
is
2 kqd
E =
3
z
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Define electric dipole moment, p
as,
r
r
p=qd
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The direction of p and d is from
the negative to positive
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E field along dipole axis at large
distances (z>>d) is
2kp
E= 3
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Electric Dipole in an E-field
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What happens when a
dipole is put in an electric
field? (com = center of
mass)
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Net force, from uniform E,
is zero
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But force on charged ends
produces a net torque
about its center of mass
Torque on an Electric Dipole
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Definition of torque
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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
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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
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U is least (greatest) when p and E are in same
(opposite) directions
Exercise
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Rank a) magnitude of torque and b) U , greatest
to least
τ = p × E = pE sin θ
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a) Magnitudes are same
U = −p • E = − pE cosθ
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U greatest at θ=180
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b) 1 & 3 tie, then 2 &4