Matter & Interactions 2nd ed. Practice Problems
Aaron Titus | High Point University
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2d30001     Electric field of a point particle; electric force     2d30001
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The high temperature of the Sun's corona ionizes iron atoms so that there are a significant number of Fe ions in the corona. (This notation indicates that a neutral iron atom has lost 11 electrons.) Suppose that an Fe ion is at the location . What is the net electric force on an electron that is at the location ?

 

2d40001     Dipole model of HCl     2d40001
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The HCl molecule is polar with a dipole moment and a negative partial charge at the chlorine atom and a net positive partial charge at the hydrogen atom. From infrared spectroscopy, the bond length of a HCl molecule is calculated to be 0.13 nm. If you model the HCl molecule as a dipole of charges and separated a distance 0.13 nm, what is the charge in the model?

 

2d40002     1-D Superposition of dipole fields along axis     2d40002
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Two dipoles are oriented as shown below. One dipole is made of opposite charges of magnitude , and the other dipole is made of opposite charges of magnitude . Both dipoles have a separation . Derive an equation for the net electric field at the point shown if the distance is much larger than the charge separation . (i.e. )


Figure: Two dipoles.

 

2f30001     Electric field along the axis of a uniformly charged thin rod     2f30001
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A thin rod of length has a uniform charge . Derive an expression for the electric field at point P on the axis of the rod that is at a distance from the center of the rod. Show that in the limit as , the electric field due to the rod is the same as if the rod is a charged particle.


Figure: Efield on the axis of a uniformly charged thin rod.

 

2m20001     Induced emf in a coil due to a changing magnetic field     2m20001
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A coil of 100 turns and radius 2 cm is in a uniform magnetic field as shown below. The magnetic field changes with time according to the graph.


Figure: A coil in a uniform magnetic field.

  1. What is the emf induced around the coil?
  2. If the coil has a resistance of , what is the current in the coil?
  3. In what direction will current flow in the coil?
  4. What is the direction of the electric field (i.e. the curly electric field) that is induced by the changing magnetic field, at point P (which is located in a +z plane, out in front of the page)?

 

2g30002     An electron deflected by charged plates.     2g30002
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An electron enters a region of uniform electric field between two closely spaced, oppositely charged plates as shown below with an initial speed of m/s. Upon exiting the region, it has been deflected upward. The horizontal displacement of the electron through the plates is 5 cm, and the plates are separated a distance 5 mm.


Figure: An electron deflected by oppositely charged plates.

  1. Sketch the electric field between the plates.
  2. Which plate is positively charged and which plate is negatively charged?
  3. Which plate is at a higher electric potential ?
  4. Sketch the path of the electron as it travels through the plates.
  5. If the vertical deflection of the electron is 1 mm, what is the potential difference across the plates?

 

2g30001     Acceleration of an alpha particle by charged plates     2g30001
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An alpha particle is accelerated by two closely spaced, oppositely charged plates, as shown below.


Figure: An alpha particle moving between oppositely charged plates.

The alpha particle has a speed of m/s when it enters a slit in the positively charged plate. After traveling for 1 mm, it passes through a slit in the negatively charged plate. If the magnitude of the charge of each plate is , and if each plate has an area of , what will be the speed of the alpha particle when it reaches the negatively charged plate? (Note: the plate separation is small compared to the dimensions of the plates.)

 

2g50001     Potential difference between points near a thin, very long, uniformly charged rod     2g50001
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A thin rod of length has a uniform charge . (a) Write an expression for the potential difference , if points A and B are very close to the rod in comparison to the length of the rod. (b) Find the potential difference if the rod's length is 1 m, the rod's charge is , point A is 1 mm from the rod, point B is 3 mm from the rod, and point C is 3 mm from the rod and 1 mm from point B.


Figure: Points near a thin, very long, uniformly charged rod.

 

2k80002     Torque on a coil     2k80002
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A coil of 20 turns of wire has a radius 0.5 cm and is connected to a power supply so that 0.4 A flows through the coil. At , the coil is at rest, current flows into the page at the top of the coil, and the plane of the coil makes an angle of with respect to a magnetic field of 0.5 T.


Figure: A coil in a uniform magnetic field.

  1. At the instant shown (t=0), what is the torque on the coil?
  2. In what direction will the loop rotate if it is released from rest?
  3. What is the magnetic potential energy of the loop at t=0?
  4. If the system is frictionless, what will be the kinetic energy of the coil when it reaches its equilibrium orientation?
  5. Describe the motion of the coil, even after a long time, if the system is frictionless.

 

2k80001     Torque on a beam     2k80001
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A 1.5-m beam has a 1-kg object hanging from its end. The beam is held in equilibrium at an angle of with respect to the horizontal, as shown below. To hold the beam in equilibrium, you grasp a handlebar of radius 2 cm at the bottom of the beam and exert a tangential force on the handlebar.


Figure: A beam in equilibrium.

  1. If the mass of the beam is negligible, what is the torque by the object on the beam, about the axis of rotation O?
  2. What magnitude force must you apply tangentially at the handlebar in order to keep the beam in equilibrium?

 


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