Please explain Your niece is considering an ambitious science fair project an el

Question

Please explain

Your niece is considering an ambitious science fair project an electrical device (which is based on magnetic concepts) used to launch a non-conducting marble. As shown in the figure, a battery is connected to two metal wires (rails) which are bridged by a sliding conducting carriage. This completes a current-carrying circuit. (The rails continue far off to the right, but do not connect to each other anywhere) sliding metal carriage metal rail non-conducting marble metal rail a) Assume that the circuit is powered by a 12 V car battery. All the resistance in the circuit comes primarily from the sliding joint between the carriage and the rails, and is in total a constant 2.5 2. The rails are 60 cm apart. How much current runs around the circuit? Indicate the current direction on the diagram (2 pts). b) indicate the direction of the magnetic field between the two rails on the diagram. Using our simple formula for the magnetic field from a long wire, what is the magnitude of the magnetic field exactly halfway between the rails? (2 pts)

Explanation / Answer

part A:

from ohms law V = iR

so current i = V/R

i = 12/2.5

i = 4.8 Amps

direction of current i = CCW

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since current is CCW,

magnetic field will be out of gthe page

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magnetic field B = uoi/2piR

here R = 60./2 = 30 cm

so

B = (2 e -7 * 4.8)/(0.3)

B = 3.2 uT

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