*9.  ssm Suppose that the light bulb in Figure 22.4b is a 60.0-W bulb with a resistance of 240 Ω. 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. What is the shortest distance along the rails that the rod would have to slide for the bulb to remain lit for one-half second?

 

We have the rate of using energy by the light bulb, that is 60.0 W which means it uses 60.0 J for each second.  So we can find the force that is being exerted on the rod by using the magnetic force which must be balanced by the hand’s force. The magnetic force is

 

 

We need the current, which we can get from the Power expression

 

Solving for i

So the force needed is

 

 

Now we use work mechanically is

 

Solving for distance

 

 

Alternatively, you could find the speed from the induced emf formula and use distance is speed times time.

 

 

 

We can get emf from another version of electrical power

 

So emf is

We find speed is

 

 

As we found before!

 

 

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This page last updated on June 24, 2018