The diagram shows a section of wire that has been positioned at 90 degrees to a 0.1-tesla magnetic field. The wire carries a current of two amperes. What is the direction of the force acting on the wire due to the magnetic field?
In our diagram, we see this section of wire with current in it pointing towards the top of the screen. Our current-carrying wire exists in a magnetic field B pointing towards the right. Our question asks us to identify the direction of the force that acts on the wire due to the magnetic field. We know that the current in this wire is due to the movement of microscopically small objects that have an electric charge. As each individual charged object moves through the magnetic field B, it experiences a magnetic force.
The direction of that force is given by something called a right-hand rule. Say that we have an object with a charge 𝑞, and imagine further that this object moves to the right with the velocity 𝑣. If our moving charge passes through a uniform magnetic field, call it B, then we can use our right hand to determine the direction of the magnetic force acting on the charge 𝑞. To do this, we point the fingers on our right hand in the direction of 𝑞 times 𝑣. If we assume that the charge 𝑞 is a positive value, then 𝑞 times 𝑣 here points to the right. Next, we curl the fingers on our right hand in the direction of the magnetic field B. We see that here that direction is into the screen. Having done all this, the thumb on our right hand now points in the direction of the magnetic force on the charge 𝑞.
The right-hand rule as we’ve described it here applies to individual charges, but we can still apply this rule to our current-carrying wire because the current consists of individual charges. If we find the direction of the magnetic force on one of these charges, that will be the same as the direction of that force on any other charges with the same sign. We are shown that current in this wire travels from the bottom towards the top of our screen. Conventionally, current is defined as the flow of positive charge. Therefore, for our current-carrying wire, 𝑞 times 𝑣 points towards the top of the screen.
We also see that the magnetic field B points towards the right. What we’ll do then is arrange our right hand so that our fingers can point upward in the direction of 𝑞 times 𝑣 but also be able to curl in this direction so that they can point in the direction of the magnetic field B. For our right hand to be able to do this, it does take a little bit of twisting. When we’re able to do it, though, our hand is arranged so that our thumb points into the screen. We know this then to be the direction of the magnetic force acting on the positive charges in the current. And this tells us the answer to our question. The direction of the force acting on the wire due to the magnetic field is into the screen.