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 ?

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?

92 1-D Superposition of dipole fields along axis 92

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.

93 Electric field along the axis of a uniformly charged thin rod 93

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.

94 Acceleration of an alpha particle by charged plates 94

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.)

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.

Sketch the electric field between the plates.

Which plate is positively charged and which plate is negatively charged?

Which plate is at a higher electric potential ?

Sketch the path of the electron as it travels through the plates.

If the vertical deflection of the electron is 1 mm, what is the potential difference across the plates?

96 Potential difference between points near a thin, very long, uniformly charged rod 96

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.

97 Acceleration of an alpha particle by charged plates 97

A proton is at the origin and is moving in the +y direction with a speed of m/s, as shown below. What is the magnetic field at each of the points shown? Note: the points are symmetric, the distance between points C and E is , and the distance between points B and C is .

Figure: Find the magnetic field at various points around a moving charged particle.

98 Deflection of a compass needle by a dipole magnet 98

A dipole magnet and compass are arranged as shown below, with the dipole aligned East-West with the compass. The dipole moment of the magnet is and its center is 20 cm from the center of a compass. The magnetic field of Earth is shown.

Sketch and calculate the deflection of the compass needle from North.

If you replace the magnetic dipole with a thin coil of radius 2 cm and 20 turns at the same location, what must be the current in the coil to give the same deflection of the compass needle as the dipole magnet?

Figure: Dipole magnet and compass.

99 Deflection of a compass needle by a dipole magnet 99

Derive an expression for the magnetic field at the center of a solenoid with N turns (or loops) of wire, length L, and current I. If the length of the solenoid is much greater than its radius R, show that the magnetic field at the center is