The upper portion of the circuit in the figure below is fixed. The horizontal wi
ID: 1430349 • Letter: T
Question
The upper portion of the circuit in the figure below is fixed. The horizontal wire at the bottom has a mass of 10.0 g and is 5.00 cm long. The wire hangs in the gravitational field of Earth form identical like springs connected to the upper portion of the circuit. The springs stretch 0.50 cm under the weight of the wire, and the circuit has a total resistance of 12.0 Omega. When a magnetic field is turned on, directed out of the page, the springs stretch an additional 0.30 cm. Only the horizontal wine at the bottom of the circuit is in the magnetic field. What is the magnitude of the magnetic field?Explanation / Answer
when there is no magnetic field, making the net force on the horizontal wire = 0, we get : mg = 2kx
=> 10*10-3*10 = 2*k*0.5*10-2 => k = 10 N/m
As the manetic field is turned on, due to current (= V/I = 24/12 = 2 Amp) flowing from left to right in the wire and the direction of magnetic field, a downward force BIL is also present on the wire, => mg + BIL = 2kx' where x' = 0.8 cm in this case
=> 0.1 + B*2*5*10-2 = 2*10*0.8*10-2 => B = 0.6 T
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