Motion In Electric Field

A positively charged plastic sphere of mass $m = 3 \times 10^{-16}$ kg is stationary between two horizontal metal plates with opposite charges. The distance between the plates is $d = 3.2$ cm. Assume $g = 10$ m/s².

In a vacuum, a pair of parallel metal plates are separated by 5.6 cm, with a voltage of 50 V applied between them. A doubly-charged oxygen ion is accelerated from rest by the electric field.

An alpha particle (charge $q_\alpha = 2e$, mass $m = 6.7 \times 10^{-27}$ kg) is fired from a great distance with an initial speed $v_i = 1.6 \times 10^7$ m/s towards a stationary gold nucleus (charge $q_{Au} = 79e$).

In a hydrogen atom, the distance between the electron and the proton in the ground state is $r = 5.29 \times 10^{-11}$ m. The energy required to move the electron from its ground state to an infinite distance is the ionization energy.

An electron, starting from rest, is accelerated by a voltage of $V_a = 100$ V. It then enters a uniform deflecting electric field of strength $E = 5000$ N/C in a direction perpendicular to the field. The length of the deflecting plates is $L = 6$ cm.

A proton with charge $+e$ and mass $m_p$ enters a uniform electric field between parallel plates with an initial velocity $v_0$. The velocity is perpendicular to the electric field lines. The plates have length $l$, are separated by a distance $d$, and have a voltage $U$ across them.

As shown in the figure, a uniform electric field has vertical equipotential surfaces at -200 V, 0 V, and 200 V, each separated by $d = 1$ cm. A small ball of mass $m = 10$ g is launched from the 0 V line with an initial velocity $v_0 = 1$ m/s at an angle of 45° to the horizontal. The ball moves in a straight line. Use $g = 10$ m/s$^2$.

A light string of length $l$ is fixed at its upper end. From its lower end hangs a charged small ball of mass $m$. The system is placed in a uniform horizontal electric field of magnitude $E$. At equilibrium, the string makes an angle $\alpha$ with the vertical, with the ball displaced in the direction of the field.

Two charged particles enter a charged parallel-plate capacitor with velocities parallel to the plates. Gravity is neglected. Both particles exit through the far end of the capacitor with the same deflection angle. Which of the following initial conditions must they satisfy?

In Fig.~12.58, two parallel metal plates are separated by a distance $d$ and have voltage $U$ applied across them, with plate $A$ at higher potential. A small piece of radioactive material on plate $A$ continuously emits $\alpha$-particles (mass $m$, charge $q$) isotropically into the right hemisphere (toward plate $B$). The maximum speed of the emitted $\alpha$-particles is $v$. Plate $B$ is coated with fluorescent powder that lights up where $\alpha$-particles strike it. Gravity is neglected and the $\alpha$-particles are not reflected by $B$.