Two horizontal parallel wires are separated by 5 cm; a view from above of the se

Question

Two horizontal parallel wires are separated by 5 cm; a view from above of the set-up is shown in the figure at right. The upper wire in the figure carries a current I from right to left, while the other wire carries the same amount of current in the opposite direction. A lightweight slider rests on top of the two wires. The entire apparatus is embedded in a uniform magnetic field which directed upward (out of the page in the figure). a) The slider is electrically conducting so that current flows through it from the upper wire in the figure to the lower; in which direction is the magnetic force on the slider? b) If the mass of the slider is 2 grams, the current I is 6 A, what is the magnetic field strength if the slider accelerates at 5 gees (that is, 5 times 9.8 m s^-2)?

Explanation / Answer

Hi,

In this case you have a conductor (the slider) inside an uniform magnetic field, therefore it will experience a magnetic force. The way to calculate said force is through the next equation:

F = I L x B ; where F is the magnetic force, I is the current that flows inside the conductor, L is a vector which value is equal to the lenght of the conductor (5 cm is this case) and which direction is the same as the current, and B is the uniform magnetic field.

(a) If we see the direction of the current over the conductor and the one of the magnetic field, we can see that both vectors form an angle 90° with each other and that the magnetic force should point towards the left of the page (in the -i direction), following the rules of the cross product.

Magnetic force: F = (ILB) (-i)

(b) If they give us the mass and the acceleration, we can find the net force. If we assume that the only force acting over the conductor is the magnetic one, then we will have the value of the magnetic force. Using the value of current that they give us as well as the lenght provided, we can find the value of the uniform magnetic field.

F = ma ::::::: F = (2*10-3 kg)*(5*9.8 m/s2) = 0.098 N

B = F/(IL) = (0.098 N)/( (6 A)*(5*10-2 m) ) = 0.327 T

Note: The current in the wires generates a magnetic field as well. However, as the current flows from one wire to the other using the slider as a bridge, there should be no electrical current ahead of the slider, so the influence of those magnetic fields should be minimal.

I hope it helps.

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