Question

The figure below is a top view of a rectangular thin wire loop that moves with velocity vo on a horizontal table. The friction against the table is negligible so that this motion would continue practically with the same velocity if not for crossing the boundary of the region of the uniform magnetic field B=3074 G, also shown in the figure. From our discussions in class, you know that this crossing is accompanied by the slowing down of the loop motion facilitated by the phenomenon of induction. In fact, while crossing the boundary, the loop's velocity v(t) would be changing with time t according to the equation dv - и dt T just as if the loop were experiencing the friction force with some effective parameter t. The geometrical dimensions of the loop are given: a=10 cm, b=29.5 cm, as well as its total resistance R=0.428 1 and mass m=5 g. b XX ХХХХХ XX ХХХХХХХХХХ В XXXX XX XX Х Х ХХХХХХ ХХХХХХХХ ХХХХХХХХ ХХХХХХХХ ХХХХХХХХ ХХХХХХХХ ХХХХХ ХХХХХ ХХХХХХ a R M ХХХХХ XX XX ХХХХХХ XXX ХХХХХХХХХХХХХХХХ XX ХХХХХХХХХ XXX Vo Understandably, if the velocity vo is "too low", the loop would stop before completely crossing the boundary of the magnetic field region. Find the minimum value Vmin of the velocity vo, at which the complete crossing is still possible: Vmin= cm/s. What would be the maximum magnitude Imax of the current induced in the loop corresponding to this limiting velocity?: Imax= mA.

Answer 1

If the right side of wire travels a distance à in magnetic field, the change in the magnetic flux is $ = Bxa The induced emf is. E- Bav. 11 do dt Ba dx dt The magnetic force points to the left direction B²a²v F: Iaß = JABE R Then Rm 22 Ba du dt du V ( where T- Ba Rm > du dt 11 T above equation Integrating t. dt -t S av S Into) → T T Vo Then Vy a Voe ( V = Voie CS Scanned with CamScanner

Then, the position as a function of time Sv.dt = Voit (i-e() The maximum düsplacement should be 126 Then Xmax - Vo.T - b. Then. b Voz B²a2b Rm question. Using the givers data from Vo = (3074 x 164)*(0:192 (0.245) Co.428) (5X1053) cm Voz 0.13026 m S 13.026 S The maximum current is No. a B Imax a (0.130267 (0.1) (3074 x 10 R (0.428) Imax = 9.3555 M A CS Scanned with CamScanner