The figure shows a light bulb connected to a conducting bar that moves to the right with velocity [math: v] in a magnetic field [math: B] directed into the page. The induced emf causes the bulb to glow. If the speed of the bar is increased, what happens to the light bulb?

Question

BlackTom AI · Accepted Answer

Motional emf in a conductor moving through a magnetic field is given by ε = B L v, so increasing v increases the induced emf and therefore the current and power delivered to the bulb.

1) Relevant knowledge points and concepts
- Motional emf: a straight conductor of length L moving with velocity v perpendicular to a magnetic field B has emf ε = B L v (from ε = ∮(v × B)·dl or Faraday’s law for moving circuits).
- Ohm’s law: I = ε / R, where R is the circuit resistance (assumed constant for the analysis).
- Power delivered to the bulb (brightness proxy): P = I^2 R = ε^2 / R. Higher P → brighter bulb.

2) Step-by-step reasoning
- The movable bar and rails form a loop of length L in the magnetic field. As the bar moves right with speed v through B (into the page), a motional emf is induced along the bar.
- That emf drives a current through the bulb; increasing v increases ε, increasing I and P.

3) Calculations with intermediate steps
- ε = B L v.
- I = ε / R = (B L v) / R.
- P = I^2 R = ((B L v)^2 / R^2) · R = (B^2 L^2 v^2) / R.
Thus P ∝ v^2: doubling v quadruples the electrical power delivered (neglecting temperature-dependent resistance changes).

4) Why the correct answer is correct
Because the induced emf and therefore the current and electrical power transferred to the bulb increase with v, the bulb receives more power and so glows brighter when the bar’s speed is increased.

5) Why other options are incorrect
- (a) “Appearance remains unchanged”: false because ε depends on v, so current and power change when v changes.
- (b) “Not enough information”: false because B, L, and v determine the emf; given v increases, the direction of change is determined.
- (d) “It glows dimmer”: opposite of the physical dependence ε ∝ v.

6) Conclusion
Increasing the bar’s speed increases the induced emf (ε = B L v), increasing current and power, so the bulb glows brighter. This confirms option c.

The figure shows a light bulb connected to a conducting bar that moves to the right with velocity [math: v] in a magnetic field [math: B] directed into the page. The induced emf causes the bulb to glow. If the speed of the bar is increased, what happens to the light bulb?单项选择题

类似问题

The faster a magnet's rate of change is within a coil, the higher the loop's emf (voltage) will be. This describes which law?

A generator requires a prime mover to create movement of a conductor in a magnetic field to produce an EMF (voltage)

Fleming rule for a generator is the:

The principle of operation of a generator is to [ Select ] excite rotate wind power a [ Select ] inductor magnet conductor brush in a [ Select ] open circuit magnetic field inductive closed ciruit .

The voltage generated in the Armature of a generator depends on three factors, the Flux strength , the Number of armature conductors and the Relative speed .

Faraday's Law of Electromagnetic Induction states that the induced electromotive force (EMF) in any closed circuit is equal to:

Direction of induced emf in a circuit is in accordance with law of

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单