24. Electric Force & Field; Gauss' Law

Each plate in a parallel-plate capacitor has an area of $12.5{\mathrm{cm}}^2$. and the separation between plates is $0.822\mathrm{mm}$. The magnitude of the charge on each plate is $7.43\text{mC}$. What is the magnitude of the electric field between the plates and inside the metal of the plates?

A water molecule is a dipole. If water were placed in the uniform field between capacitor plates, which of the following would best describe the force and torque experienced by the water molecules?

INT FIGURE EX23.25 shows a 1.5 g ball hanging from a string inside a parallel-plate capacitor made with 12 cm×12 cm electrodes. The electrodes are charged to ±75 nC . What is the charge on the ball in nC?

INT Electrostatic cleaners remove small dust particles and pollen grains from air by first ionizing them, then flowing the air between the plates of a parallel-plate capacitor, parallel to the plates, where electric forces deposit charged particles on one of the electrodes. A typical pollen grain has a mass of 5.0×10^−10 g, the ionizer charges it with 750 extra electrons, and a fan moves the air at 3.0 m/s. Ignore air resistance and gravity. b. What minimum electric field strength is needed to deflect the grain by 3.0 mm before it leaves the electrodes?

One type of ink-jet printer, called an electrostatic ink-jet printer, forms the letters by using deflecting electrodes to steer charged ink drops up and down vertically as the ink jet sweeps horizontally across the page. The ink jet forms 30-μm-diameter drops of ink, charges them by spraying 800,000 electrons on the surface, and shoots them toward the page at a speed of 20 m/s . Along the way, the drops pass through two horizontal, parallel electrodes that are 6.0 mm long, 4.0 mm wide, and spaced 1.0 mm apart. The distance from the center of the electrodes to the paper is 2.0 cm. To form the tallest letters, which have a height of 6.0 mm, the drops need to be deflected upward (or downward) by 3.0 mm. What electric field strength is needed between the electrodes to achieve this deflection? Ink, which consists of dye particles suspended in alcohol, has a density of 800 kg/m^3 .

CP A proton is traveling horizontally to the right at 4.50 * 10^6 m/s. (a) Find the magnitude and direction of the weakest electric field that can bring the proton uniformly to rest over a distance of 3.20 cm.

CP A proton is traveling horizontally to the right at 4.50 * 10^6 m/s. (b) How much time does it take the proton to stop after entering the field?

CP A proton is traveling horizontally to the right at 4.50 * 10^6 m/s. (c) What minimum field (magnitude and direction) would be needed to stop an electron under the conditions of part (a)?

a. Starting from rest, how long does it take an electron to move 1.0 cm in a steady electric field of magnitude 100 N/C?

INT A proton is fired horizontally into a 1.0×10^5 N/C vertical electric field. It rises 1.0 cm vertically after having traveled 5.0 cm horizontally. What was the proton's initial speed?

A 0.80-μm-diameter oil droplet is observed between two parallel electrodes spaced 11 mm apart. The droplet hangs motionless if the upper electrode is 20 V more positive than the lower electrode. The density of the oil is 885 kg/m³ . (c) Does the droplet have a surplus or a deficit of electrons? How many?

CP A uniform electric field exists in the region between two oppositely charged plane parallel plates. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate, 1.60 cm distant from the first, in a time interval of 3.20 * 10^-6 s. (b) Find the speed of the proton when it strikes the negatively charged plate.

CP A uniform electric field exists in the region between two oppositely charged plane parallel plates. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate, 1.60 cm distant from the first, in a time interval of 3.20 * 10^-6 s. (a) Find the magnitude of the electric field.

Two large, parallel conducting plates carrying op­posite charges of equal magnitude are separated by 2.20 cm. (a) If the surface charge density for each plate has magnitude 47.0 nC/m^2, what is the magnitude of E in the region between the plates?

An electron is released from rest at the center of a parallel-plate capacitor that has a 1.0 mm spacing. The electron then strikes one of the plates with a speed of 1.5×10^6 m/s. What is the electric field strength inside the capacitor?