### Video Transcript

Which of the following is the correct formula for the magnitude of the force experienced by a current-carrying wire in a uniform magnetic field? ๐น is the force experienced by the wire. ๐ is the acceleration of the wire. ๐ฟ is the length of the wire. ๐ผ is the magnitude of the current within the wire. And ๐ต is the strength of the magnetic field. (A) ๐น is equal to ๐ต times ๐ผ squared times ๐ฟ. (B) ๐น is equal to ๐ต times ๐ผ divided by ๐ฟ. (C) ๐น is equal to ๐ต divided by ๐ผ times ๐ฟ. (D) ๐ is equal to two times ๐ต divided by ๐ผ times ๐ฟ. And (E) ๐น is equal to ๐ต times ๐ผ times ๐ฟ.

In this situation, weโre imagining a wire of length ๐ฟ carrying a current of magnitude ๐ผ that exists in a magnetic field of strength ๐ต. In this situation, the current-carrying wire will experience a force and that force will increase. The longer the wire is, the greater the current in the wire is, and the stronger the magnetic field ๐ต. This fact that ๐น increases as any one of these three variables increases lets us eliminate any answer options where any of these three variables are in the denominator. For example, answer option (B) claims that as the length of the wire ๐ฟ increases, ๐น decreases. We know that thatโs not true, that rather as ๐ฟ grows, so does ๐น. So we can eliminate answer choice (B). And for the same reason, we can also eliminate answer choice (C).

Taking a look at answer choice (D), we see that this option also has ๐ผ and ๐ฟ in the denominator, but now weโre considering the acceleration of our wire rather than the force on it. Recalling Newtonโs second law of motion that the net force on an object equals the mass of that object times its acceleration, we know that in general the net force on an object is proportional to its acceleration. Therefore, we would expect that as ๐ผ and ๐ฟ increase, the acceleration of the wire would increase as well rather than decrease. We can also cross out, therefore, answer choice (D). The remaining answer options (A) and (E) are only different in the power of the current ๐ผ.

At this point, we can note that this force ๐น on a current-carrying wire in a magnetic field comes down to a force thatโs experienced by the moving charges in the current of the wire. That is, it is individual charged particles that experience this force. If we double the amount of charge passing through this wire in a given interval of time, in other words, if we double the current ๐ผ, then that means there are twice as many charges to experience this force. And therefore, the overall force is twice as big. We can say then that the overall force ๐น is proportional to the current ๐ผ. That is, itโs not the case that ๐น is proportional to ๐ผ squared as answer option (A) would claim.

For our final answer, we choose option (E). The force experienced by the wire is equal to the magnetic field strength ๐ต times the magnitude of the current ๐ผ times the length of the wire ๐ฟ.