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Unformatted text preview: 1 Magnetic Field due to a Current (Ampere’s Law) Force due to Magnetic Fields on Charges and Currents (Lorentz Force) 9/28/11 Physics 104, Fal 2011 1 Electric vs. Magnetic Electric Magnetic Source: Charges Moving Charges Act on: Charges Moving Charges Magnitude: F = q E F = q v B sin( θ ) Direction: Parallel to E Perpendicular to v,B 9/28/11 Physics 104, Fal 2011 2 September 28, 2011 Physics 104, Fal 2010 3 Currents Create B fields Lines of B Current I OUT • Direction: Thumb on I Fingers point to position Palm gives B r = distance from wire μ = 4 π × 10 − 7 Tm / A B = μ I 2 π r r Magnitude: B Ampere’s Law “Permeability of free space” September 28, 2011 Physics 104, Fal 2010 4 Two long wires carry opposite current What is the direction of the magnetic field above, and midway between the two wires carrying current? Note: this is different from the electric field made by two opposite charges. x Adding Magnetic Fields 1) Left 2) Right 3) Up 4) Down 5) Zero B x E x + - Direction & Magnitude of Magnetic Force on a Moving Charge • For a charge + q moving with velocity • Direction of magnetic force is always perpendicular to both and • F max occurs when is perpendicular to • F = 0 when is parallel to • For any angle θ between: 9/28/11 Physics 104, Fal 2011 5 v B F = qvB sin θ v v B v B Right Hand Rule • Place fingers in direction of velocity, • Curl fingers in direction of magnetic field, • Thumb points in direction of force on a positive charge, – If the charge is negative, the force is opposite that found by the right hand rule 9/28/11 Physics 104, Fal 2011 6 v B F There are several other variants of this rule – use whatever you like 2 Magnetic Fields & Force • If a test charge moves with velocity and is subject to a magnetic force, a magnetic field is said to exist. – (Similar to the way electric fields are defined) • The SI unit of magnetic field is the Tesla (T) – Unit of magnetic flux is a Weber Wb • The cgs unit of magnetic field is a Gauss (G) – 1 T = 10 4 G 9/28/11 Physics 104, Fal 2011 7 T= Wb m 2 = N C ⋅ (m/s) = N A ⋅ m B = F m qv sin θ v September 28, 2011 Physics 104, Fal 2010 8 v • B B = μ I 2 π r same F = qvB sin θ same v and B are normal in both cases: sin θ = 1 A long straight wire is carrying current from left to right. Near the wire is a charge q with velocity v I v a) r • Compare magnitude of magnetic force on q in (a) vs. (b) a) has the larger force b) has the larger force c) force is the same for (a) and (b) • r b) F F Reading Quiz F has different directions More on Magnetic Force on Moving Charges • Magnetic force on a charge depends on the magnitude of the charge, its velocity, and the magnetic field....
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