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## Homework Statement

The diagram represents a cylindrical aluminium bar AB resting on two horizontal aluminium rails which can be connected to a battery to drive a current through AB. A magnetic field, of flux density 0.10 T, acts perpendicularly to the paper and into it. In which direction will AB move if the current flows from A to B?

Calculate the angle to the horizontal to which the rails must be tilted to keep AB stationary if its mass is 5.0 g, the current in it is 4.0 A and the direction of the field remains unchanged.

(Acceleration of free fall, g = 10 m s

^{-2}.)

Answer: 21.8 °

**2. The attempt at a solution**

"In which direction will AB move?"

Is this question asking about the direction of the force? If yes, what direction of field should be taken? On the left side the field is directed towards the paper (since current goes from A to B) and on the right side the current goes out of the paper.

I tried to calculate the angle but I didn't get the correct answer.

Φ = AB cos θ, where AB is the length of the cylinder.

Φ = B A, where Φ is magnetic flux, B is the magnetic field and A is the area of a circle.

B = m g / I L = [(5 / 1000) * 10] / [4 * (5 / 100)] = 0.25 T, we found the magnetic field first.

A = π r

^{2}, this is the formula for the area of a circle, we still lack the radius.

B = μ

_{0}I / 2 π r → r = μ

_{0}I / 2 π B = (4 π * 10

^{-7}* 4) / 2 π * 0.25 = 3.2 * 10

^{-6}m, we found the radius from the magnetic field formula.

A = π * (3.2 * 10

^{-6})

^{2}= 3.2 * 10

^{-11}m

^{2}, we found the area of a circle.

Φ = 0.25 * 3.2 * 10

^{-11}= 8.042 * 10

^{-12}Wb, we found the magnetic flux.

cos θ = 8.042 * 10

^{-12}/ 0.05 → θ = 89.9 °, we found the angle.

What's missing?