Question Video: Calculating the Acceleration of a Current-Carrying Wire | Nagwa Question Video: Calculating the Acceleration of a Current-Carrying Wire | Nagwa

Question Video: Calculating the Acceleration of a Current-Carrying Wire Physics • Third Year of Secondary School

A 1 m long wire carrying a current of 5 A is positioned at 90° to a 0.1 T magnetic field. The mass of the wire is 25 g. How quickly does the wire accelerate?

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Video Transcript

A one-meter-long wire carrying a current of five amperes is positioned at 90 degrees to a 0.1-tesla magnetic field. The mass of the wire is 25 grams. How quickly does the wire accelerate?

Let’s say that this is our wire, with length 𝐿, carrying a current, we’ll call 𝐼, of five amperes, all in a magnetic field 𝐵 of strength 0.1 teslas that points perpendicularly to the wire. Given all this, we want to solve for the wire’s acceleration. The fact that the wire will accelerate implies that there will be a net force acting on it. Indeed, when a length of wire 𝐿 carrying a current 𝐼 exists in a uniform magnetic field 𝐵, then when that magnetic field is perpendicular to the wire, as it is in our case, the force that acts on the wire equals 𝐵 times 𝐼 times 𝐿. We could think of this as a force that acts on the moving charges in the wire’s current.

Using this equation, we can solve for the force 𝐹 on the wire, but it’s the acceleration of the wire that we’re really interested in. We can now recall Newton’s second law of motion, which says that the net force on an object equals that object’s mass times its acceleration. Combining these equations, we get this result. The mass of the wire times its acceleration equals the magnetic field strength 𝐵 times the current in the wire 𝐼 multiplied by the wire’s length 𝐿.

Dividing both sides of this equation by the mass of the wire so that that factor cancels on the left, we find that the wire’s acceleration equals 𝐵 times 𝐼 times 𝐿 divided by 𝑚. We know the values of all the quantities on the right side of this expression, so we can substitute those in now. The magnetic field strength 𝐵 is 0.1 teslas, the current 𝐼 is five amperes, the length 𝐿 is one meter, and the mass of the wire is 25 grams.

Before we calculate the acceleration 𝑎 though, we’ll want to make a units conversion. To make all of the units in our expression consistent, we’ll want to convert our mass, which is currently in grams, into the SI base unit of mass, the kilogram. One gram, we know, is equal to one one thousandth of a kilogram. So, to convert this number in grams into a number in kilograms, we’ll divide it by 1000. 25 divided by 1000 is the same as 0.025. We’re now ready to calculate the acceleration 𝑎. It’s equal to exactly 20 meters per second squared. This is how quickly the wire accelerates.

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