Magnetic Force and Electric Field Problems

The specific principles required are indicated in italics at the beginning of each problem.

1. Magnetic Force: You are working on a project to make a more efficient engine. Your team is investigating the possibility of making electrically controlled valves that open and close the input and exhaust openings for an internal combustion engine. Your assignment is to determine the stability of the valve by calculating the force on each of its sides and the net force on the valve. The valve is made of a thin but strong rectangular piece of non-magnetic material that has a loop of current carrying wire along its edges. The rectangle is 0.35 cm x 1.83 cm. The valve is placed in a uniform magnetic field of 0.15 T such that the field lies in the plane of the valve and is parallel to the short sides of the rectangle. The region with the magnetic field is slightly larger than the valve. When a switch is closed, a 1.7 A current enters the short side of the rectangle on one side of the valve and leaves on the opposite side. To give different currents through the wires along the long sides of the valve, a resistor is inserted into the wire on each of these sides. The value of the resistor on one side is twice that on the other side.
   
   
2. Magnetic Force: You have landed a great summer job in the medical school assisting in a research group investigating short lived radioactive isotopes which might be useful in fighting cancer. Your group is working on a way of transporting alpha particles (Helium nuclei) from where they are made to another room where they will collide with other material to form the isotopes. Since the radioactive isotopes are not expected to live very long, it is important to know precisely how much time it will take to transport the alpha particles. Your job is to design that part of the transport system which will deflect the beam of alpha particles (m = 6.64 x 10-27 kg, q = 3.2 x 10-19 C) through an angle of 90o by using a magnetic field. The beam will be traveling horizontally in an evacuated tube. At the place the tube is to make a 90o turn you decide to put a dipole magnet which provides a uniform vertical magnetic field of 0.030 T. Your design has a tube of the appropriate shape between the poles of the magnet. Before you submit your design for consideration, you must determine how long the alpha particles will spend in the uniform magnetic field in order to make the 90o-turn.
   
   
3. Magnetic Force: You've just learned about the earth's magnetic field and how a compass works and you are relaxing in front of the TV. Tired of your show, you think about how the picture tube works in relation to what you have learned. In a typical color picture tube for a TV, the electrons are boiled off of a cathode at the back of the tube and are accelerated through about 20,000 volts towards the picture tube screen. On the screen is a grid of ``color dots'' about 1/100 inch apart. When the electrons hit them, the dots scintillate their appropriate colors producing the color picture. Without taking apart the set, you determine whether the manufacturer needed to shield the color picture tube from the earth's magnetic field?
   
   

4. Magnetic Field (Biot-Savert Law): You are continually having troubles with the CRT screen of your computer and wonder if it is due to magnetic fields from the power lines running in your building. A blueprint of the building shows that the nearest power line is as shown below. Your CRT screen is located at point P. Calculate the magnetic field at P as a function of the current I and the distances a and b. Segments BC and AD are arcs of concentric circles. Segments AB and DC are straight-line segments.

5. Magnetic Field - Amphere's Law: While studying intensely for your physics final you decide to take a break and listen to your stereo. As you unwind, your thoughts drift to newspaper stories about the dangers of household magnetic fields on the body. You examine your stereo wires and find that most of them are coaxial cable, a thin conducting wire at the center surrounded by an insulator, which is in turn surrounded by a conducting shell. The inner wire and the conducting shell are both part of the circuit with the same current (I) passing through both, but in opposite directions. As a way to practice for your physics final you decide to calculate the magnetic field in the insulator, and outside the coaxial cable as a function of the current and the distance from the center of the cable. As an additional challenge to yourself, you calculate what the magnetic field would be (as a function of the current and the distance from the center of the cable) inside the outer conducting shell of the coaxial cable. For this you assume that the inner radius of the conducting shell is R1 and the outer radius is R2.
   
   
6. Magnetic Force - Faraday's Law: You have a summer job working at a company developing systems to safely lower large loads down ramps. Your team is investigating a magnetic system by modeling it in the laboratory. The safety system is a conducting bar that slides on two parallel conducting rails that run down the ramp. The bar is perpendicular to the rails and is in contact with them. At the bottom of the ramp, the two rails are connected together. The bar slides down the rails through a vertical uniform magnetic field. The magnetic field is supposed to cause the bar to slide down the ramp at a constant velocity even when friction between the bar and the rails is negligible. Before setting up the laboratory model, your task is to calculate the constant velocity of the bar sliding down the ramp on rails in a vertical magnetic field as a function of the mass of the bar, the strength of the magnetic field, the angle of the ramp from the horizontal, the length of the bar which is the same as the distance between the tracks, and the resistance of the bar. Assume that all of the other conductors in the system have a much smaller resistance than the bar.