7.4 Magnetic Force on a Current-Carrying Conductor
Learning Objectives
By the end of this section, you will be able to:
Determine the direction in which a current-carrying wire experiences a force in an external magnetic field
Calculate the force on a current-carrying wire in an external magnetic field
Force on a Current-Carrying Wire
In this circuit, a portion of the wire is immersed in a magnetic field. The length of the wire that is in the field is ℓ. The field has a strength B and points out of the page (as seen from the dots, like a bunch of darts coming right at you, yikes!). Every charge in this wire feels a force from the magnetic field.
Here is a RHR check:
Going back to our definition of conventional current (I = flow of positive charges), what is the direction of the magnetic force on these moving charges?
Practice!
In the following series of questions, there is a current-carrying straight wire segment (with connecting wires up and out of the page that are not shown) in a uniform magnetic field directed out of the page.
Practice 7.4.1
First, what is the direction of the magnetic force acting on the wire segment due to the uniform magnetic field?
Check your answer: A. upward
Practice 7.4.2
What would the direction of the magnetic force acting on the wire segment be if the direction of the uniform magnetic field were into the page?
Check your answer: B. downward
Practice 7.4.3
What would the direction of the magnetic force acting on the wire segment be if we reversed the direction of the current in the wire segment (assuming the B-field is still out of the page)?
Check your answer: B. downward
Practice 7.4.4
What would happen to the magnitude of the magnetic force acting on the wire segment if the wire segment were longer but still completely within the uniform magnetic field?
Check your answer: C. The force would increase.
Practice 7.4.5
What would happen to the magnitude of the magnetic force acting on the wire segment if the wire segment were moved without changing its orientation so that its length was half-in and half-out of the uniform magnetic field region?
Check your answer: B. The force would decrease.
Discuss!
The figure shows a top view of two conducting rails on which a conducting bar can slide. A uniform magnetic field is directed perpendicular to the plane of the figure as shown (into the page, X). A battery is to be connected to the two rails so that when it’s connected, current will flow through the bar and cause a magnetic force to push the bar to the right.
In which orientation, A or B, should the battery be placed in the circuit to result in a magnetic force on the bar that pushes it to the right?
Pause & Predict 7.4.1
What is the current in the wire if the magnetic force is equal to the gravitational force on the wire?
Pause & Predict 7.4.2
What is the angle between the magnetic dipole moment and the magnetic field?
Practice!
Practice 7.4.6
A 65-cm segment of conducting wire carries a current of 0.35 A. The wire is placed in a uniform magnetic field that has a magnitude of 1.24 T. What is the angle between the wire segment and the magnetic field if the force on the wire is 0.26 N?
Check your answer: C. 67°
Practice 7.4.7
Two long straight wires are parallel to each other and are separated by 78 mm. The current in wire 1 is 3.55 A and the current in wire 2 is 2.75 A. What is the force per unit length between the two wires?
Check your answer: A. 2.5 x 10-5 N/m
Practice 7.4.8
A circular coil of conducting wire, with a radius of 4.48 cm and 25 turns, is in a 1.67-T magnetic field. When the coil’s dipole moment vector makes an angle of 34° with the magnetic field, a 0.537-N•m torque is exerted on the coil. What is the current in the coil?
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