28. Magnetic Fields and Forces

Singly ionized (one electron removed) atoms are accelerated and then passed through a velocity selector consisting of perpendicular electric and magnetic fields. The electric field is 155 V/m and the magnetic field is 0.0315 T. The ions next enter a uniform magnetic field of magnitude 0.0175 T that is oriented perpendicular to their velocity. (a) How fast are the ions moving when they emerge from the velocity selector? (b) If the radius of the path of the ions in the second magnetic field is 17.5 cm, what is their mass?

A 150 g ball containing 4.00 x 10⁸ excess electrons is dropped into a 125 m vertical shaft. At the bottom of the shaft, the ball suddenly enters a uniform horizontal magnetic field that has magnitude 0.250 T and direction from east to west. If air resistance is negligibly small, find the magnitude and direction of the force that this magnetic field exerts on the ball just as it enters the field.

An open plastic soda bottle with an opening diameter of 2.5 cm is placed on a table. A uniform 1.75 T magnetic field directed upward and oriented 25° from vertical encompasses the bottle. What is the total magnetic flux through the plastic of the soda bottle?

A horizontal rectangular surface has dimensions 2.80 cm by 3.20 cm and is in a uniform magnetic field that is directed at an angle of 30.0° above the horizontal. What must the magnitude of the magnetic field be to produce a flux of 3.10 x 10^-4 Wb through the surface?

A circular area with a radius of 6.50 cm lies in the xy-plane. What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field B = 0.230 T at an angle of 53.1° from the +z-direction?

A flat, square surface with side length $3.40\mathrm{cm}$ is in the xy-plane at $z=0$. Calculate the magnitude of the flux through this surface produced by a magnetic field $B=\left(0.200T\right)i+\left(0.300T\right)j-\left(0.500T\right)k$.

An electron experiences a magnetic force of magnitude 4.60 x10^-15 N when moving at an angle of 60.0° with respect to a magnetic field of magnitude 3.50 x 10^-3 T. Find the speed of the electron.

A particle with mass $1.81\times {10}^{-3}$ $\mathrm{kg}$ and a charge of $1.22\times {10}^{-8}\text{ C}$ has, at a given instant, a velocity $v=(3.00\times {10}^4\text{ m/s})j$. What are the magnitude and direction of the particle's acceleration produced by a uniform magnetic field $B=\left(1.63T\right)i+\left(0.980T\right)j$?

The heart produces a weak magnetic field that can be used to diagnose certain heart problems. It is a dipole field produced by a current loop in the outer layers of the heart. What is the magnitude of the heart's magnetic dipole moment?

A 150 V battery is connected across two parallel metal plates of area 28.5 cm² and separation 8.20 mm. A beam of alpha particles (charge +2e, mass 6.64 x 10^-27 kg) is accelerated from rest through a potential difference of 1.75 kV and enters the region between the plates perpendicular to the electric field, as shown in Fig. E27.29. What magnitude and direction of magnetic field are needed so that the alpha particles emerge undeflected from between the plates?

The Hall effect can be used to measure blood flow speed because the blood contains ions that constitute an electric current. (a) Does the sign of the ions influence the emf? Explain. (b) Determine the flow speed in an artery 3.3 mm in diameter if the measured emf across the width of the artery is 0.13 mV and B is 0.070 T. (In actual practice, an alternating magnetic field is used.)

A long copper strip is 3.0 cm wide and thick. When it carries a steady 42-A current in a 0.80-T magnetic field it produces a 6.5-μV Hall emf. Determine:

(a) the Hall field in the conductor;

(b) the drift speed of the conduction electrons;

(c) the density of free electrons in the metal.

A Hall probe, consisting of a rectangular slab of current-carrying material, is calibrated by placing it in a known magnetic field of magnitude 0.10 T. When the field is oriented normal to the slab’s rectangular face, a Hall emf of 12 mV is measured across the slab’s width. The probe is then placed in a magnetic field of unknown magnitude B, and a Hall emf of 63 mV is measured. Determine B assuming that the angle θ between the unknown field and the plane of the slab’s rectangular face is (a) θ = 90°, and (b) θ = 60°.

Consider an electron undergoing cyclotron motion in a magnetic field. According to Bohr, the electron’s angular momentum must be quantized in units of ℏ. Compute the first four allowed radii in a 1.0 T magnetic field.