# Force Required to Push a Wire

1. Homework Statement

The 10-cm-wide, zero-resistance slide wire shown in the figure is pushed toward the 2.0$$\Omega$$resistor at a steady speed of 0.50 m/s. The magnetic field strength is 0.50 T. A) How big is the pushing force?
B) How much power does the pushing force supply to the wire?
C) What is the magnitude of the induced current?
D) How much power is dissipated in the resistor?

2. Homework Equations

$$F_{push} = \frac{v L^2 B^2}{R}$$

$$P_{input} = F_{push}*v = \frac{v^2 L^2 B^2}{R}$$

3. The Attempt at a Solution

A) $$F_{push} = \frac{v L^2 B^2}{R} = \frac{(0.5) (0.1)^2 (0.5)^2}{2} = 6.25 * 10^{-4} N$$

B) $$P_{input} = F_{push}*v = \frac{v^2 L^2 B^2}{R} = \frac{(0.5)^2 (0.1)^2 (0.5)^2}{2} = 3.125 * 10^4 W$$

C) $$I = \frac{vLB}{R} = \frac{(0.5)((0.1)(0.5)}{2} = 1.25 * 10^2 A$$

D) $$P_{dissipated} = P_{input} = 3.125 * 10^4 W$$

Did I make any mistakes?

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I am working on exactly same one.

I used I=E/R=(vLB)/R equation to solve C, and had 0.0125A or 1.25*10^-2

but they said it's not quite. :-(

Anyway, there is another question: What is the direction of the induced current?

I know I need to use the right hand rule but can't apply it right.

Is it clockwise or counterclockwise? anyone can explain?

The induced current opposes the change in magnetic flux through the loop. As you push the bar to the right you are decreasing the amount of "out of the page" magnetic field so the loop creates a current that would result in MORE magnetic field "out of the page".

Put your hand in the "thumbs up" position and point your thumb in the direction of the magnetic field you want to create...right now, "out of the page". The direction your fingers curl is the direction of the induced current. (ie along your fingers towards your fingernails.

man, still confused with "out of the page"

but.. okay. somewhat got it...

Still, nobody for part C ?

dmsgo89, I'm pretty sure your answer for C is correct, or is at least the answer I got. Check your significant figures though.