lecture9 - 9 Lecture 9 9.1 Magnetic forces on an electric...

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9. Lecture 9 9.1 Magnetic forces on an electric current Since an electric current is charges in motion it follows that a wire through which a current circulates will experience a force in the presence of a magnetic field. In fact an interesting demo (fig.52) makes this e ff ect evident. More precisely, suppose that, inside the conductor, an electric charge density (charge per unit volume) ρ is moving with velocity v . Then, during time t all the charge contained in a volume v tA will pass through a cross section of area A as can be seen in fig.53. The electric current, namely the amount of charge going through a section of the conductor of area A per unit time is therefore I = Q t = ρ v tA t = ρ vA (9.1) On the other hand the magnetic force on a moving charge is | F | = q | v || B | sin θ = ρ AL | v || B | sin θ = IL | B | sin θ (9.2) where we used that the total charge is given by q = ρ LA for a conductor of length L . Therefore the force is proportional to the current and the length, one can define a force per unit length as | F | L = I | B | sin θ (9.3) The direction and orientation of the force is given by exactly the same right-hand rule as before. Only that instead of the velocity we use the direction of the current. A very interesting observation is that the magnetic field allows to determine the sign of the charge density ρ responsible for the current. This is illustrated in fig.54 and known as the Hall e ff ect. The same current can be produced by positive carriers moving in one direction along a wire or by negative ones moving in the opposite direction. However, the magnetic force on the wire is the same in both cases and for that purpose we do not need to know the sign of the carriers. On the other hand it means that the carriers would like to accumulate on one side of the wire and therefore if that side becomes positively charged the carriers are positive and if it becomes negatively charged they are negative. The experiment shows that the carriers are negative as we
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