28. Magnetic Fields and Forces

An electron in a cathode-ray tube is accelerated through a potential difference of 10 kV, then passes through the 2.0-cm-wide region of uniform magnetic field in FIGURE P29.60. What field strength will deflect the electron by 10°?

An antiproton (same properties as a proton except that q = -e) is moving in the combined electric and magnetic fields of FIGURE P29.61. What are the magnitude and direction of the antiproton's acceleration at this instant?

A 65-cm-diameter cyclotron uses a 500 V oscillating potential difference between the dees. What is the maximum kinetic energy of a proton if the magnetic field strength is 0.75 T?

A proton moving in a uniform magnetic field with ${\vec{v}}_1=(1.00\times {10}^6\hat{i})\text{m/s}$ experiences force ${\vec{F}}_1=(1.20\times {10}^{-16}\hat{k})\text{N}$. A second proton with ${\vec{v}}_2=(2.0\times {10}^6\hat{j})\text{m/s}$ experiences ${\vec{F}}_2=(-4.16\times {10}^{-16}\hat{k})\text{N}$ in the same field. What is $\vec{B}$? Give your answer as a magnitude and an angle measured counter-clockwise from the $+x$-axis.

The uniform 30 mT magnetic field in FIGURE P29.65 points in the positive z-direction. An electron enters the region of magnetic field with a speed of 5.0 x 10⁶ m/s and at an angle of 30° above the xy-plane. Find the radius r and the pitch p of the electron's spiral trajectory.

To five significant figures, what are the cyclotron frequencies in a 3.0000 T magnetic field of the ions (a) O₂⁺, (b) N₂⁺, and (c) CO⁺? The atomic masses are shown in the table; the mass of the missing electron is less than 0.001 u and is not relevant at this level of precision. Although N₂⁺ and CO⁺ both have a nominal molecular mass of 28, they are easily distinguished by virtue of their slightly different cyclotron frequencies. Use the following constants: 1 u = 1.6605 x 10⁻²⁷ kg, e = 1.6022 x 10⁻¹⁹ C.

Radio astronomers detect electromagnetic radiation at 45 MHz from an interstellar gas cloud. They suspect this radiation is emitted by electrons spiraling in a magnetic field. What is the magnetic field strength inside the gas cloud?

A proton moves in the magnetic field B = 0.50 î T with a speed of 1.0 x 10⁷ m/s in the directions shown in FIGURE EX29.27. For each, what is magnetic force F on the proton? Give your answers in component form.

An electron travels with $\vec{v}=(5.0\times {10}^6\hat{i})\text{m/s}$ through a point in space where $\vec{E}=(2.0\times {10}^5\hat{i}-2.0\times {10}^5\hat{j})\text{V/m}$ and $\vec{B}=-0.10\hat{k}\text{T}$. What is the force on the electron?

What is the force (magnitude and direction) on the proton in FIGURE P31.28? Give the direction as an angle cw or ccw from vertical.

A rocket cruises past a laboratory at 1.00×10⁶ m/s in the positive x-direction just as a proton is launched with velocity (in the laboratory frame) $\vec{v}=(1.41\times {10}^6\hat{i}+1.41\times {10}^6\hat{j})$ m/s. What are the proton's speed and its angle from the y-axis in the rocket frame?

A proton is fired with a speed of 1.0×10⁶ m/s through the parallel-plate capacitor shown in FIGURE P31.29. The capacitor's electric field is E =(1.0×10⁵ V/m, down). How does an experimenter in the proton's frame explain that the proton experiences no force as the charged plates fly by?

Muons ( mass = 207 times the electron mass, same charge -e ) are accelerated horizontally by 65 kV. They then pass through a uniform magnetic field B for a distance of 3.8 cm, which deflects them upward so they reach a detector 22 cm away, 11 cm above their original direction. Estimate the value of B.

A 3.40-g bullet moves with a speed of 155 m/s perpendicular to the Earth’s magnetic field of 5.00 x 10⁻^-5 T. If the bullet possesses a net charge of 18.5 x 10^-9 C, by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.25 km?