Magnetic Field Inducing Electric Field - Lighting a 60W Bulb

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Homework Help Overview

The discussion revolves around a problem involving electromagnetic induction, specifically how a magnetic field can induce an electric field sufficient to light a 60W bulb. The parameters include the bulb's resistance, the magnetic field strength, and the length of a rod sliding on rails.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of Faraday's law of induction and the relationship between induced emf, magnetic flux, and circuit parameters. Questions arise regarding the necessary velocity and rail length to maintain the bulb's illumination.

Discussion Status

Some participants have provided insights into the relationships between emf, current, and resistance, while others express uncertainty about the calculus involved and the lack of certain parameters like velocity. There is an ongoing exploration of how to relate the given information to find a solution.

Contextual Notes

Participants note the absence of velocity information, which is crucial for determining the required rail length. The problem constraints focus on maintaining the bulb's illumination for a specific duration.

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Suppose the light bulb in Figure 22.4b is a 60.0-W bulb with a resistance of 240 W. The magnetic field has a magnitude of 0.40 T, and the length of the rod is 0.60 m. The only resistance in the circuit is that due to the bulb. Minimally, how long would the rails on which the moving rod slides have to be, in order that the bulb can remain lit for one-half second?

Anyone know how i can start going about solving this :)?
 

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Faraday's law states that the induced emf is equal to the negative rate of change of magnetic flux. Also the rate of change of magnetic flux is equal to B*dA/dt, since the magnetic field is completely perpendicular to the entire area.

Emf = B*dA/dt, you can relate this to the information given in the problem

remember that emf = I*R
 
please help me..
i don't know much calculus

P = V^2/R
im assuming V = emf in the equation emf = vBL
so

60W = emf^2/240ohms
emf = 120V..

but they do not give me a velocity or anything
im stumped :/
 
The using that V = vBL you can solve for velocity. You already calculated V and B and L are given.

Assuming the velocity is constant you can just multiply 1/2 a second to find the rail length.
 

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