Torque on a Current Loop in a Uniform Magnetic Field

Torque on a Current Loop in a Uniform Magnetic Field -...

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Physics 202 Tuesday, March 30, 1999 Announcements: None Lecture notes: Torque on a Current Loop in a Uniform Magnetic Field We said the net force on a current loop in a constant magnetic field is zero, but the torque is not necessarily zero! o F = i (L (cross product) B) o Case One Net Force = 0 Net Torque = 0 τ = r (cross) F o Case Two Net Force = 0 Net Torque does not equal zero
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o Define axis of rotation: through ED, then τ = (a) (i) (b) B If Area of loop = A = ab, then τ = (a) (i) (b) B = i AB Through OF, τ = (1/2)(a) (i) (b) B + (1/2)a i b B = i AB Resolve B into 2 components o Bsin θ perpendicular to normal o Bcos θ along the normal (no torque) o The component of B that's perpendicular to normal ( in the Bsin θ plane of the loop) gives the force F = i b Bsin θ τ = i b Bsin θ a = iABsin θ = i(A (cross product) B) o It is convenient to define a vector quantity for the area of the loop o Area vector points along the normal of the loop o
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