How does a charged particle move in a uniform magnetic field? How would this mot

Question

How does a charged particle move in a uniform magnetic field? How would this motion change if the velocity had a component parallel to the field? How can we use the Biot-Savart law to calculate the magnetic field of a long straight current carrying wire? How would you use this result to determine the magnetic field generated by two parallel wires? Two perpendicular wires? What law/method for calculating E does this remind you of? Extension problem This also works with a circular wire. Use this method to find the magnetic field at an arbitrary point on the axis running through the center of the hoop. You can assume that the hoop is carrying a steady current I and has a radius R. How can we use Ampere's law to calculate the magnetic field of a long straight current carrying wire? Does it agree with the result you got using the Biot-Savart Law for the same current geometry? What law/method for calculating E does this remind you of? Extension problem Use this method to find the magnetic field of an infinitely long thick wire. You can assume the wire is carrying a current I and has a thickness R. You will very likely find sample problems similar to these in any introductory physics textbook. On the test, you can expect a few questions about a Helmholtz Coil. An alternate way of finding a magnetic field in highly symmetric situations using Ampere's law (Equation 28.20, p. 935): integral_closed loop B middot dl = mu_0 I_enc (a) Compare this law to Gauss' Law integral E middot dA = Q_enc/0 from electrostatics. What is similar about the equations? What is different? (b) Assume that we have an infinitely long, straight wire, carrying a constant current I, and we want to find the magnetic field a distance s away from the "center" of that wire. Be sure to label the direction that the current is flowing and the distance s. (c) Use the right hand rule to determine the direction of the magnetic field at the given point. (d) In your sketch above draw an appropriate Amperian loop that you will integrate over. (e) Do the above integral, and solve for the magnitude of the field at the point indicated. (f) Does your answer match the result from the previous problem? Which method was easier?

Explanation / Answer

Q1.

force on a moving charge in a magnetic field is given by

force=charge*cross product of velocity and magnetic field

so if velocity is not parallel to magnetic field, force is non-zero.

if velocity is perpendicular to magnetic field,

force is perpendicular to both velocity and magnetic field and hence the charge will follow a circular path.

part b:

if velocity has a parallel component, force due to parallel component is zero.

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