Learning Goal: To understand the force on a charge moving in a magnetic field. M

Question

Learning Goal:

To understand the force on a charge moving in a magnetic field.

Magnets exert forces on other magnets even though they are separated by some distance. Usually the force on a magnet (or piece of magnetized matter) is pictured as the interaction of that magnet with themagnetic field at its location (the field being generated by other magnets or currents). More fundamentally, the force arises from the interaction of individual moving charges within a magnet with the local magnetic field. This force is written F =qv ×B , where F  is the force, q is the individual charge (which can be negative), v  is its velocity, and B  is the local magnetic field.

This force is nonintuitive, as it involves the vector product (or cross product) of the vectors v  and B . In the following questions we assume that the coordinate system being used has the conventional arrangement of the axes, such that it satisfies i^×j^=k^, where i^, j^, and k^ are the unit vectors along the respective axes (x, y and z). (Figure 1)

Part F

Now consider the case in which the positive charge q is moving in theyz plane with a speed v at an angle with the z axis as shown (Figure 2) (with the magnetic field still in the +z direction with magnitude B). Find the magnetic force F  on the charge.

Express the magnetic force in terms of given variables like q, v, B, , and unit vectors.

Part C

Now consider the example of a positive charge q moving in the xyplane with velocity v =vcos()i^+vsin()j^ (i.e., with magnitude vat angle with respect to the x axis). If the local magnetic field is in the +z direction, what is the direction of the magnetic force acting on the particle?

Express the direction of the force in terms of , as a linear combination of unit vectors, i^, j^, and k^.

figure 1

Figure 2

Explanation / Answer

c) Find the cross product

F mg = -cos(theta) j + sin(theta) i

f)

a) Direction of F = i cap

v perp = vsin(theta) j cap

F = qvBsin(theta) i cap

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.