A metal rod slides along rails in a magnetic field. Closing the switch connects the rod, rails, and resistor into 1 complete circuit.
Adjust conditions:
The sliders adjust the values
速さが半分になるまでに、初めの運動エネルギーの何％が熱になる？
初めから回路を開いたままなら、0.693秒後の棒の速さは？
The equations explain the phenomenon
1The force on an electron is determined as the rod moves through a magnetic field.F=e v B……
2The electric potential difference between the ends is determined when the electric and magnetic forces balance.V=v B L……
3The circuit is closed, and the electromotive force is expressed in terms of the rate of change of magnetic flux.|ℰ|=|dΦdt|……
4The force on the current-carrying rod determines the sign of the electromotive force.ℰ=−dΦdt……
5The force on the current-carrying rod is included in the equation of motion.m dvdt=−(B L)² vR……
6The equation of motion is rewritten as an equation for the change in energy.−d(½ m v²)dt=R I²……
7Integration over time gives the fraction of energy converted to heat when the speed falls to half its initial value.Q=½ m v₀² − ½ m v²，Q½ m v₀²=1 − (vv₀)²……
8A magnet approaches a stationary coil, illustrating induction by an electric field.∮ E · dl=−dΦdt……
Further development: using electromagnetic induction to generate and transmit alternating current
9The induced electromotive force is determined from the change in the coil's own electric current.ℰ=−L dIdt……
10A rotating coil generates alternating current.ℰ=B S ω sin ωt……
11The shared magnetic flux determines the relationship between the number of turns and the voltage.V₂V₁=N₂N₁……
12The equivalent direct voltage produces the same average heating power in the same resistor.Ve=V₀√2……
13The reduction in transmission losses is determined when the same power is transmitted at a higher voltage.Transmission losses=R (PV)²［W］……
What this chapter has shown
Electric charges in a moving rod experience a magnetic force. Closing the circuit allows an electric current to flow, and the rod slows under a force opposing its motion. The lost kinetic energy is converted to Joule heating in the resistor. In a stationary coil, electric charges are moved by the electric field produced by a changing magnetic field.
75％This is the rate at which energy is converted to heat in a closed circuit
If the circuit is open from the start, no electric current flows, the rod continues at 1.0 m/s, and the heat generated is 0 J.
In everyday lifeSome train braking systems use the motors as generators, producing electricity as the train slows down.
Detailed summary
When a conductor moves through a magnetic field, the Lorentz force pushes electrons within it toward one side, producing an electromotive force. Its magnitude equals the rate of change of magnetic flux, and its direction opposes that change. All the kinetic energy lost is converted into Joule heating. When the magnet moves instead, a new physical fact must be recognized: a changing magnetic field produces an electric field. Alternating current and transformers make direct use of this electromagnetic induction.