What is the rule used to determine the direction of the magnetic force on a straight current-carrying wire placed in a magnetic field?
Let’s start out on our solution by making a simple sketch of the straight current-carrying wire in a magnetic field. Here we have our wire. And we’ll say that it carries current in this direction. The wire exists in a uniform magnetic field which is running perpendicular to the axis of the wire.
We know that the current that this wire carries consists of charge in motion. And therefore, since we have moving charges in the presence of a magnetic field, we know those charges experience a magnetic force. And since the charges are carried by the wire, the wire experiences a magnetic force. And it’s the direction of that force that we want to solve for.
To figure out force direction in cases like this, we can do it actually using our left hand. With this hand, if we put our index finger in the direction of the magnetic field and then point our remaining fingers in the direction perpendicular to our forefinger, where the remaining fingers Point in the direction of the current that flows through the wire. And then pointing our thumb perpendicular to our forefinger as well as our remaining fingers, then the direction of our thumb indicates the direction of the magnetic force on the current-carrying wire. This method is called Fleming’s left-hand rule.
Let’s try out this rule by applying it to the scenario that we’ve sketched. Our first step is to use our left hand and point our index finger in the direction of the magnetic field. We see the magnetic field is pointed this way. Then we take our remaining three fingers and we point them in the direction of the current as it flows along the current-carrying wire. That’s in this direction. And then, finally, we point our thumb perpendicular to both our forefinger and the rest of our fingers. That would be in this direction here. According to our rule, the direction of our thumb indicates the direction of the magnetic force acting on the current-carrying wire. It acts up on the wire.
So to figure out the direction of the magnetic force acting on a straight current-carrying wire that’s in a magnetic field, we can use the rule known as Fleming’s left-hand rule.