2) An infinite long wire carries a current 𝑖ô€¯ôˆºð‘¡ôˆ» ô€µ...

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2) An infinite long wire carries a current 𝑖􀯐􁈺𝑡􁈻 􀵌 𝑖􀯢 cos􁈺𝜔𝑡􁈻. Nearby, there is a triangular loop at a distance 𝑐 from the long wire, with base 𝑏 and height 𝑎. The loop has electrical resistance R. [Express answers in terms of 𝑎, 𝑏, 𝑐, 𝑅, 𝑖0, 𝑡 and 􀊘 as appropriate] (a) (5 pts) At which instants in time is there zero induced current in the loop, during the range 0 􀵑 𝑡 􀵑 2𝜋/𝜔? (b) (5 pts) When is the induced current flowing clockwise as viewed in the figure, during the range 0 􀵑 𝑡 􀵑 2𝜋/𝜔? (c) (11 pts) What is the magnitude of the induced current in the loop? Express your answer as a function of time t. (d) (3 pts each part) For your convenience, the same exact figure on the previous page is repeated here What is the direction of the force on the loop when: (i􁈻 𝑡 􀵌 0? Circle one: (no force, attracted to wire, repelled by wire) (ii) 𝑡 􀵌 𝜋/􁈺4𝜔􁈻? Circle one: (no force, attracted to wire, repelled by wire) (iii) 𝑡 􀵌 𝜋/􁈺2𝜔􁈻? Circle one: (no force, attracted to wire, repelled by wire) 3) Consider the circuit shown below, where the EMF of the battery is 𝜀 􀵌 5.00 V, 𝑅1 􀵌 𝑅2 􀵌 10.0 Ω and 𝑅3 􀵌 5.00 Ω, 𝐿 􀵌 10.0 μH and 𝐶 􀵌 40.0 μF. The capacitor starts out uncharged and the inductor is not energized in any way. Assume that all wires shown connecting these components are perfect ideal conductors. You must show all your work! (a) (6 pts) At time 𝑡 􀵌 0, the switch S1 is closed while switch S2 remains open. Immediately after this, what is the potential difference across resistor 𝑅1? (b) (6 pts) After a very long time with switch S1 closed and switch S2 open, what is the current through 𝑅3? (c) (4 pts) After a very long time with S1 closed and S2 open, the switch S1 is opened and simultaneously switch S2 is closed. Immediately after this, what is the potential difference 𝑉􀮺 􀵆 𝑉􀮻 as labelled in the figure? (d) (6 pts) How many seconds after S2 is closed will the magnitude of the charge on the capaciator first be at its maximum? (e) (8 pts) What is the maximum magnitude of the charge on the capaciator? When it first reaches that maximum, what will be the potential difference 𝑉􀮺 􀵆 𝑉􀮻?

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