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05:10Suppose the Earth’s magnetic field at the equator has magnitude 0.50 x 10⁻⁴ T and a northerly direction at all points. Estimate the speed a singly ionized uranium ion ( m = 238 u, q = e) would need to circle the Earth 5.0 km above the equator. Can you ignore gravity? [Ignore relativity.]
Suppose the electric field between the electric plates in the mass spectrometer of Fig. 27–34 is 2.84 x 10⁴ V/m and the magnetic fields are B = B'= 0.58 T. The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by 1.67 x 10⁻²⁷ kg.) Does it matter if the ion charge is positive (lost electrons) or negative (gained electrons)? Explain.
Suppose the electric field between the electric plates in the mass spectrometer of Fig. 27–34 is 2.84 x 10⁴ V/m and the magnetic fields are B = B'= 0.58 T. The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by 1.67 x 10⁻²⁷ kg .) How far apart are the marks formed by the singly charged ions of each type on a detector or photographic film? What if the ions were doubly charged?
A uniform conducting rod of length ℓ and mass m sits atop a fulcrum, which is placed a distance ℓ/4 from the rod’s left-hand end and is immersed in a uniform magnetic field of magnitude B directed into the page (Fig. 27–54). An object whose mass M is 7.0 times greater than the rod’s mass is hung from the rod’s left-hand end. What current (direction and magnitude) should flow through the rod in order for it to be “balanced” (i.e., be at rest horizontally) on the fulcrum? (Flexible connecting wires which exert negligible force on the rod are not shown.)
The magnetic field B at the center of a circular coil of wire carrying a current I (as in Fig. 27–9) is B = (μ₀NI) / 2r where N is the number of loops in the coil and r is its radius. Imagine a simple model in which the Earth’s magnetic field of about 1 G ( = 1 x 10⁻⁴ T) near the poles is produced by a single current loop around the equator. Roughly estimate the current this loop would carry.
A mass spectrometer is monitoring air pollutants. It is difficult, however, to separate molecules of nearly equal mass such as CO (28.0106 u) and N₂ (28.0134 u). How large a radius of curvature must a spectrometer have (Fig. 27–34) if these two molecules are to be separated on the detector by 0.50 mm?
