LECT14_194197

LECT14_194197 - 19.4: Force on a Current-carrying Conductor...

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Unformatted text preview: 19.4: Force on a Current-carrying Conductor Total force = Force on each charge # of charges in the wire F B = (q v dr B sin ) (n A l ) (A l = vol.; n = charges/vol) But recall that I = Q/ T and Q/ T = (q of each charge) (# of charges per second) # of charges per second = A n v dr (m 2 ) (m-3 ) (m/s) So I = n A v dr q F B = B I l sin( ) or F B / l = B I sin( ) Reminder: Direction of deflection is given by right hand rule: I = thumb B = fingers F B = out of your palm Example: Your magnet produces a B-field with strength 0.01 T in the plane of the page as shown. A wire carries 1 Amp from left to right, such that = 30. What's the force per unit length (and its direction)? F B / l = B I sin30 = 0.01T 1A 0.5 = 0.005 N/m (out of page) So it's not much. Suppose the current is 6 Amps and the B-field is 3 T. F B / l = 9 N/m (which is slightly more substantial) B I 30 Consider a power transmission line carrying 100 Amps from W to E. What's the total force on 100m of wire due to the Earth's magnetic field (assume a North component only)? In which direction is the wire deflected (assume charge carriers are e 's)? Reminder: the Earth's B-field is 0.5 Gauss = 0.5 10-4 T F B = B I l sin = (0.5 10-4 T)(100A)(100m) = 0.5 N. So, again, it's not much. Direction of deflection = downward Force on a square loop of current in a uniform B-field. F top = 0 ( = 180; sin = 0; so F B = 0) F bottom = 0 F left = I b B (out of page) F right = I b B (into page) Assume loop is on a frictionless axis Whats the TORQUE on the current loop? Fig. 19.15b in text is the view along the axis, from the bottom towards the top. Reminder: torque = F r = F r sin = F left a/2 + F right a/2 = (B b I + B b I) a/2 = B I A A = area; =90 here Note direction of torque: clockwise For 1 loop: = BIA sin max = BIA For N turns: Total current = NI = BIAN sin Magnetic Moment = IAN always points perp. to the plane of the loops (points along the normal) = B sin A coil consisting of 100 turns, each carrying 3A of current and having an area 0.2 m 2 , is oriented such that its normal makes a...
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LECT14_194197 - 19.4: Force on a Current-carrying Conductor...

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