- #1

TFM

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## Homework Statement

A vertical square loop of copper wire with sides of length 100 mm is falling from a region where the magnetic field is horizontal and of magnitude 1.2 T into a region where the field is zero, as shown in the diagram below. The diameter of the copper wire is 1 mm.

[The resistivity of copper is [tex] 1.7 x 10^{-8} \Ohm[/tex] m; the density of copper is 8960 kg m-3.]

(i) Calculate the magnitude of the current round the loop, in terms of the velocity of fall v, and indicate its sense.

(ii) What is the magnetic force acting on the loop, again expressed in terms of v?

(iii) If the velocity of fall reaches a steady value whilst the upper arm of the circuit remains in the field, calculate this velocity.

## Homework Equations

V = IR

[tex] R = \rho \frac{l}{A} [/tex]

[tex] \epsilon = -\frac{d\Phi_B}{dt} [/tex]

[tex] \Phi = BA [/tex]

## The Attempt at a Solution

Okay I am on the first part I have calculated the Current like so:

Area of each 'side' = 0.001 x 0.1 = 0.0001m x 4 sides = 0.0004m^2

[tex] \Phi_B = 1.2 * 0.0004 = 0.00048 [/tex]

[tex] \epsilon = -\frac{\Delta\Phi_B}{\Delta T} = \frac{0.00048}{\frac{0.1}{v}} = 0.0048v[/tex]

V = IR:

I = V/R, using

[tex] R = \rho \frac{l}{A} [/tex]

l = 0.4m

A = [tex] \pi * (0.0005)^2 = 7.85 * 10^{-7}[/tex]

[tex] R = 1.7 * 10^{-8}zfrac{0.4}{7.85 * 10^{-7}} = 8.66 * 10^{-3} \Ohms [/tex]

[tex] I = \frac{V}{R} = \frac{0.0048v}{8.66 * 10^{-5}} = 0.554v Amps [/tex]

The thing I am uncertain on at the moment is what is the sense? I haven't heard of this term before?

Any ideas?

TFM