The problem involvesa small loop of wire which is stuck inside a larger coil. Th
ID: 1263531 • Letter: T
Question
The problem involvesa small loop of wire which is stuck inside a larger coil. The loop has a resistance of 0.5 ohms and is1.0 cm in diameter. It is stuck inside a coil that is 2.0 cm in diameter. The coil has 120 turns and itis 8.0 cm in length. The current in the coil varies with time s shown in the diagram. When lookinginto the coil from the left, a positive current is seen to be clockwise. Your assignment is todetermine the current in the single loop when t=10.0 ms. You need to state the direction of thecurrent as well, but you knew that!
The problem involvesa small loop of wire which is stuck inside a larger coil. The loop has a resistance of 0.5 ohms and is1.0 cm in diameter. It is stuck inside a coil that is 2.0 cm in diameter. The coil has 120 turns and itis 8.0 cm in length. The current in the coil varies with time s shown in the diagram. When lookinginto the coil from the left, a positive current is seen to be clockwise. Your assignment is todetermine the current in the single loop when t=10.0 ms. You need to state the direction of thecurrent as well, but you knew that!Explanation / Answer
The magnetic field due tot he coil is
B(t) = uo N I(t) / L
Here,
I(t) = 0.5 - 50t
Thus,
dB/dt = uo N (-50) / L
As the emf in the loop is
emf = A dB/dt,
and for the small loop, r = 0.5 cm.
Thus, A = pi r^2 = 7.8540E-5 m^2, then
emf = 7.40E-6 V
Thus,
I = emf / Resistance = 1.48*10^-5 A [ANSWER]
As it has to oppose the changing flux, the current is COUNTERCLOCKWISE from our view. [ANSWER]
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