Work done by the magnetic field on the resistor

[syhpui2]

Homework Statement

A magnetic field, B= 0.8 T, is directed out of the page in a region containing a rectangular up-side-down "U-wire" having width W = 0.5 m, as shown. A resistor of mass m and resistance R = 6 Ω, which is free to slide without friction on the vertical rails, is released from rest and starts falling in the presence of the Earth's gravitational field, reaching a terminal speed v = 3.8 m/s.

http://i.imgur.com/ukw8m.png


Which statement(s) below is (are) valid during the time the resistor is falling at terminal velocity?

(a) The work per unit time done by the Earth on the resistor is equal to the power dissipated in the resistor.

(b) The work done by the magnetic field on the resistor is equal in magnitude, but opposite in sign, to the work done by the Earth on the resistor.

(c) Both of the statements above are valid.


Correct Answer: C

Homework Equations

P=UI

The Attempt at a Solution

I tried to analyze with P=UI. However, I get answer B. Should I analyze it with W=Fd?

 

[anathema]

it is important to consider both the equations and the physical concepts involved in a problem. In this case, both P=UI and W=Fd can be used to analyze the situation.

Using P=UI, we can see that the power dissipated in the resistor is equal to the work done by the Earth on the resistor. This is because the power dissipated in the resistor is equal to the product of the current (I) and voltage (U), which is also equal to the rate at which energy is transferred by the Earth's gravitational field to the resistor as it falls. Therefore, statement (a) is valid.

Using W=Fd, we can see that the work done by the magnetic field on the resistor is equal in magnitude, but opposite in sign, to the work done by the Earth on the resistor. This is because the magnetic force on the resistor is perpendicular to the direction of motion, and therefore does no work. Instead, the work done by the magnetic field is in the form of changing the direction of the resistor's motion, which is opposite to the work done by the Earth's gravitational field. Therefore, statement (b) is also valid.

In conclusion, both statements (a) and (b) are valid during the time the resistor is falling at terminal velocity. It is important for scientists to consider both the equations and physical concepts involved in a problem to fully understand and analyze a situation.