Homework 5

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1) An electron gun fires electrons into a magnetic field directed towards the center of Earth. Find the direction of the force exerted by the field on an electron for each of the following directions of the electron's velocity: (a) horizontal and due north; (b) horizontal and 30o west of north; (c) due north, but 30o below the horizontal; (d) straight upward

 

 

 

 

2) (a) Find the direction of the force on a proton moving through the magnetic fields (blue vector) as in figure below. The velocity of the proton is designated with the red vector. (b) Repeat part (a), assuming the moving particle is an electron.

 

 

12) In figure of problem 2a assume that in each case the velocity vector shown is replaced with a wire carrying a current in the direction of the velocity vector. For each case, find the directions of the magnetic force acting on the wire.

 

 

 

4) Determine the initial direction of the deflection of charged particles as they enter the magnetic fields, as shown in figure.

 

 

 

 

10) Sodium ions (Na+) move at 0.851 m/s through a bloodstream in the arm of a person standing near a large magnet. The magnetic field has a strength of 0.254 T and makes an angle of 51o with the motion of the sodium ions. The arm contains 100 cm3 of blood with 3.00x1020 Na+ ions per cubic centimeter. If no other ions were present in the arm, what would be the magnetic force on the arm?

 

 

 

29) The figure shows a diagram of a device called a velocity selector, in which particles of a specific velocity pass through un-deflected while those with greater or lesser velocities are deflected either upwards or downwards. An electric field is directed perpendicular to a magnetic field. When the electric and magnetic forces on a charged particle are equal and opposite in direction, they cancel out and the particles pass through un-deflected. Show that particles with speed of v = E/B will pass through the velocity selector un-deflected.

 

 

30) Consider the mass spectrometer shown schematically. The electric field between the plates of the velocity selector is 950N/C. The magnetic field in both the velocity selector area and the deflection chamber is of magnitude of 0.930 T. Calculate the radius of the path in the system for a singly charged ion with mass m = 2.18x10-26 kg. (Hint: See problem 29)

 

 

 

35) A lightning bolt may carry a current of 1.00x104 A for a short time. What is the resulting magnetic field 100 m from the bolt? Suppose the bolt extends far above and below the point of observation.

 

 

 

 

45) A wire with a weight per unit length of 0.080 N/m is suspended directly above a second wire. The top wire carries a current of 30.0 A and the bottom wire carries a current of 60.0 A. Find the distance of separation between the wires so that the top wire will be held in place by magnetic repulsion. See example 7 from lesson 5.