Answer to Question #89725 in Electric Circuits for Nathaniel Brima Vandi

Question

(1) With a speed of 0,15m/s moves a 2,4dm long conductor perpendicular to the field lines in a field flow density is 28mT. how much voltage is induced in the conductor?
(2) a car runs at a speed of 90km / h on a horizontal wall where the earth magnetic field is 52µT and the angle of inclination is 68. how much voltage is induced between the ends of a 1.6m long axis?
(3) Two parallel metal plates are in a vacuum. the voltage between the plates is 5.7kV, according to a small plastic ball with a mass of 44mg falls at a constant speed in space between the plates. the distance between the plates is 1.7cm. calculate the ball charge

Answer 1

1) If the length of the conductor is 2.4 decimeters, or 24 cm, the induced voltage will be

$$V=vBl\text{sin}90^\circ=0.15\cdot0.24\cdot0.028=0.001\text{ V, or 1 mV}.$$

2) Convert km/h to m/s:

$$u=v\frac{1000}{3600}=90\frac{1000}{3600}=25\text{ m/s}.$$

$$V=uBl\text{sin}68^\circ,$$

$$V=25\cdot1.6\cdot52\cdot10^{-6}\cdot0.93=1.93\cdot10^{-3}\text{ V, or 1.93 mV}.$$

3) The magnetic field between the plates is

$$E=\frac{V}{d}.$$

According to Newton's second law, since the ball moves with constant speed, all forces are balanced, or mathematically:

$$F_\text{electric}=F_\text{gravitational},$$

$$Eq=mg,$$

$$q=\frac{mg}{E}=\frac{mgd}{V},$$

$$q=\frac{44\cdot10^{-6}\cdot9.81\cdot0.017}{5700}=1.29\cdot10^{-9}\text{ C, or 1.29 nC}.$$