? Because of the voltage u between bc, the induced electromotive force is 43U.
Let the magnetic induction intensity be B, then: 43U = BLV … ①
△t 1 time, the average induced electromotive force e =△φ△ t1= BLD△ t1… ②
Solve ① ② simultaneously to get E = 4UD3V △ T 1.
(2) According to the image, the magnitude of electromotive force increases uniformly with time, the velocity v increases uniformly with time according to E=BLv, and the wireframe makes uniform acceleration of linear motion.
Let the acceleration a of the wire frame, the velocity v when bc side enters the magnetic field, △t 1=△t2=2△t3=2△t, the length l of the wire frame and the width d of the magnetic field,
According to the displacement of the wireframe in three time periods
v？ 2△t+ 12a(2△t)2=d
v？ 4△t+ 12a(4△t)2=L
v？ 5△t+ 12a(5△t)2=L+d
The solution is LD = 187.
(3) If only an initial speed v0 is given to the coil, so that the coil can slide freely to the right, a single-turn square coil will be subjected to an ampere force to the left and decelerate to the right, and the ampere force will decrease with the decrease of the speed, so the coil will decelerate to the right with a reduced acceleration, but the following situations may occur.
In the first case, if v0 is relatively small, the velocity will decrease to zero before bc reaches the right boundary of the magnetic field, and then it will remain stationary, as shown in Figure A. 。
In the second case, when the bc side reaches the right boundary of the magnetic field, the speed has not dropped to zero, so the magnetic flux passing through the coil does not change, there is no induced current, and the coil moves in a straight line at a uniform speed. When the ad side enters the magnetic field, it will receive an ampere force to the left and then decelerate to acceleration.
There are two situations when the ad edge enters the magnetic field to decelerate: First, the speed may drop to zero before the ad edge reaches the right boundary of the magnetic field, as shown in Figure B; Second, it is possible that when the ad side reaches the right boundary of the magnetic field, the speed has not dropped to zero, and then there is no force in the horizontal direction, and the coil moves at a uniform speed, as shown in Figure C. 。
Therefore, if only an initial velocity v0 is given to the coil, so that the coil can slide freely to the right, then v-t images will appear in the following three situations because the bc side of the coil enters the magnetic field.
Answer: (1) If the rotation speed of the coil measured when the bc side of the coil just enters the magnetic field is V, and the voltage between two points bc is U, find the time of △t 1, and the average induced electromotive force in the coil is E = 4UD3V △ T 1.
(2) If △ t1:△ t2: △ t3 = 2: 2:1,the ratio of the side length of the wire frame to the width of the magnetic field is 18: 7.
(3) If only an initial velocity v0 is given to the coil, the coil can slide freely to the right, and a v-t image will appear after the coil bc enters the magnetic field, as shown in the above figures A, B and C..