The angle θ is 90 degrees, which means sin θ = 1. For part a, since the current and magnetic field are perpendicular in this problem, we can simplify the formula to give us the magnitude and find the direction through the RHR-1. The magnetic force on a current-carrying wire in a magnetic field is given by F → = I l → × B →. (a) If a constant magnetic field of magnitude 0.30 T is directed along the positive x-axis, what is the magnetic force per unit length on the wire? (b) If a constant magnetic field of 0.30 T is directed 30 degrees from the + x-axis towards the + y-axis, what is the magnetic force per unit length on the wire? If the charge carriers move with drift velocity v → d, v → d, the current I in the wire is (from Current and Resistance)Ĭalculating Magnetic Force on a Current-Carrying WireĪ long, rigid wire lying along the y-axis carries a 5.0-A current flowing in the positive y-direction. The wire is formed from material that contains n charge carriers per unit volume, so the number of charge carriers in the section is n A The length and cross-sectional area of the section are dl and A, respectively, so its volume is V = A To investigate this force, let’s consider the infinitesimal section of wire as shown in Figure 11.12. A current-carrying wire in a magnetic field must therefore experience a force due to the field. Calculating the Magnetic ForceĮlectric current is an ordered movement of charge. (b) A long and straight wire creates a field with magnetic field lines forming circular loops. Note the symbols used for the field pointing inward (like the tail of an arrow) and the field pointing outward (like the tip of an arrow). A composite sketch of the magnetic circles is shown in Figure 11.11, where the field strength is shown to decrease as you get farther from the wire by loops that are farther separated.įigure 11.11 (a) When the wire is in the plane of the paper, the field is perpendicular to the paper. An arrow pointed away from you, from your perspective, would look like a cross or an ×. These symbols come from considering a vector arrow: An arrow pointed toward you, from your perspective, would look like a dot or the tip of an arrow. If the magnetic field were going into the page, we represent this with an ×.
If the magnetic field were coming at you or out of the page, we represent this with a dot. In RHR-2, your thumb points in the direction of the current while your fingers wrap around the wire, pointing in the direction of the magnetic field produced ( Figure 11.11). To determine the direction of the magnetic field generated from a wire, we use a second right-hand rule. Therefore, a current-carrying wire produces circular loops of magnetic field. The compass needle near the wire experiences a force that aligns the needle tangent to a circle around the wire. (This connection between electricity and magnetism is discussed in more detail in Sources of Magnetic Fields.) A connection was established that electrical currents produce magnetic fields. When discussing historical discoveries in magnetism, we mentioned Oersted’s finding that a wire carrying an electrical current caused a nearby compass to deflect. Magnetic Fields Produced by Electrical Currents We are studying two separate effects here that interact closely: A current-carrying wire generates a magnetic field and the magnetic field exerts a force on the current-carrying wire. However, before we discuss the force exerted on a current by a magnetic field, we first examine the magnetic field generated by an electric current. If these moving charges are in a wire-that is, if the wire is carrying a current-the wire should also experience a force.
Moving charges experience a force in a magnetic field. Calculate the force on a current-carrying wire in an external magnetic field.Determine the direction in which a current-carrying wire experiences a force in an external magnetic field.By the end of this section, you will be able to: