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

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

Whenever magnetic flux linked with a coil changes, induced EMF in circuit will change

Calculate the emf when a coil of 100 turns is subjected to a flux rate of 0.3 tesla/sec.

Doubling the time a loop of wire takes to rotate in an electrical generator produces what effect on the induced EMF, assuming all other factors remain constant?

Doubling the strength of the magnetic field through a loop of wire produces what kind of change on the induced emf, assuming all other factors remain constant?

A 3.6V light bulb is connected to a square loop of wire that measures 69cm per side. The loop is oriented perpendicular to a magnetic field with initial magnitude 2.2T. The magnetic field drops to zero over time Δ t. Find Δ t so that the bulb lights up with the specified potential difference.

The emf induced in a generator is due to the change in:

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