You are tapping a T-money card and putting it away from the subway sensor. This scenario is approximated as in the following diagram, where the sensor is represented by an infinite straight wire with a current I and the card by a rectangular loop of wires ( N turns, size: h imes w ). The wires have a tiny gap of width a(a≪h), which is connected by a resistor (resistance R ). Your card is separated by x from the sensor.
(1) What is the magnetic field B produced by the wire?
(2) Find the mutual flux and the inductance.
(3) If x is fixed and I(t)=I_(0)sin2pi ft, what is the induced electromotive force V_(l) across the resistor? Specify the polarity
(4) If x=x_(0)+vt ( x_(0) : initial separation, v : velocity, and t : time) and current is fixed at I= I_(0), what is the induced electromotive force V_(2) across the resistor? Specify its polarity.
You are tapping a T-money card and putting it away from the subway sensor. This scenario is approximated as in the following diagram, where the sensor is represented by an infinite straight wire with a current I and the card by a rectangular loop of wires (N turns, size: h w). The wires have a tiny gap of width a (a < h), which is connected by a resistor (resistance R). Your card is separated by x from the sensor.
Nturns
W
Subway sensor
Your card
(1) What is the magnetic field B produced by the wire? (2) Find the mutual flux and the inductance. (3) Ifx is fixed and I(t) = Iosin2nft, what is the induced electromotive force Vi across the resistor? Specify the polarity (4) If x = xo + vt (xo: initial separation, v: velocity, and t: time) and current is fixed at I = Io, what is the induced electromotive force V2 across the resistor? Specify its polarity