A charged particle accelerated to a velocity v enters the chamber of a mass spectrometer. The particle’s velocity is perpendicular to the direction of the uniform magnetic field B in the chamber. After the particle enters the magnetic field, its path is a 1. parabola. 2. circle. 3. spiral. 4. straight line. Answer: 2. The magnetic force on the particle is perpendicular to both the magnetic field and the particle’s velocity. Thus, its path is circular.

Example: Determine the direction of the force for each of the following situations. Up Into the page Left Down No Force

Electrons are emitted at the left of the device shown in the photograph at the left above. As they move from left to right in the partially evacuated tube, they pass through a defining slit and are rendered visible when the resulting beam strikes a fluorescent screen, as seen in the close-up photograph at the right. A bar magnet will now be moved close to the electron beam, with the North end of the magnet closest to the tube, so the magnetic field lines are pointed away from the viewer into the picture. What will happen to the path of the electron beam as the magnet is moved close to the tube? The electron beam will: (1) deflect upward. (2) deflect downward. (3) deflect into the picture. (4) deflect out of the picture. (5) remain moving along the same line.

3. both positive and negative. 4. need more information A CuSO4 solution is placed in a container housing coaxial cylindrical copper electrodes. Electric and magnetic fields are set up as shown. Uncharged pollen grains added to the solution are carried along by the mobile ions in the liquid. Viewed from above, the pollen between the electrodes circulates clockwise. The pollen is carried by ions that are 1. positive. 2. negative. 3. both positive and negative. 4. need more information B B Answer: 3. Positive ions move radially inward due to the electric field between the cylinders. In the presence of the magnetic field, the right-hand rule indicates that they circulate clockwise. Negative ions move radially outward, but because of their negative charge, the right-hand rule gives a clockwise circulation for them too. E E

Example: A particle is positively charged to 10 mC and moving at a velocity of 2000 m/s to the right through an external magnetic field with a strength of 5 x 104 T directed into the page. What is the magnetic force acting on the charge? What path would the charge follow if left in the magnetic field for a long time? What would the net force on the charge be if there was also an electric field of 2 x 107 V/m directed downward? q = 90o, sin90o = 1 a) Up b) The charge will follow a circular path. c) down Up

We do not always only look at a single moving charge We do not always only look at a single moving charge. Often we consider multiple charges, which is typically described as a current. The previous force equation can be modified to account for multiple charges. Force on a current carrying wire Microscopic view of current through a wire N is the number of charges present. Similarly, The quantity L is the length vector parallel to the wire that points in the direction of current flow. Current is not a vector!

Example: A square loop of wire with sides 20 cm long is placed in an external uniform magnetic field with a strength of 5 T directed out of the page. If a current of 5 A flows clockwise in the loop, what is the force on the right edge of the circuit? 1 Left Force on each side of the loop is directed towards the center of the circuit! The example above has the magnetic field perpendicular to the plane containing the circuit. What happens if the magnetic field is parallel to the plane containing the loop? Force on the top and bottom of the loop would be zero. Force on the left and right sides of the loop would not be zero. 1 Left: Into the page 1 Right: Out of the page