The figure shows electrons 1 and 2 on an x axis and charged ions 3 and 4 of identical charge −q and at identical angles θ. Electron 2 is free to move; the other three particles are fixed in place and are intended to hold electron 2 in place. For physically possible values of q ≤ 5e, what are the (a) smallest, (b) second smallest, and (c) third smallest values of θ for which electron 2 is held in place? (a) Number Units (b) Number Units (c) Number Units
In the figure above, particles 1 and 2 are fixed in place, but particle 3 is free to move. If the net electrostatic force on particle 3 due to particles 1 and 2 is zero, what is the ratio q1 q2 in terms of L12 and L23? q1/q2 =
An electron has an initial velocity of (15.9 j^ + 18.9 k^) km/s, and a constant acceleration of (1.58×1012 m/s2) i^ in the positive x direction in a region in which uniform electric and magnetic fields are present. If B^ = (522 μT)i^ find the electric field E^.
An ion has a mass of 5.45×10−25 kg and a charge of +5e. What is the magnitude of the electric field that will balance the gravitational force on the particle?
During their lifetime, a person will consume approximately 1.2×104 gallons of water. An Olympic-size swimming pool, which has a volume of 2.5 million liters (L), can provide a lifetime of water for how many people? Recall that 1 gallon (gal) = 3.785×10−3 m3, and 1 mL = 10−6 m3. Number Units
A sound wave with a frequency of 12.4 kHz emerges through a circular opening that has a diameter of 0.187 m. Find the diffraction angle θ when the sound travels (a) in air and (b) in water. (Note: The speed of sound in air is 343 m/s and the speed of sound in water is 1482 m/s.) (a) Number Units (b) Number Units
The membrane that surrounds a certain type of living cell has a surface area of 5.5×10−9 m2 and a thickness of 1.1×10−8 m. Assume that the membrane behaves like a parallel plate capacitor and has a dielectric constant of 4.4. (a) The potential on the outer surface of the membrane is +71.8 mV greater than that on the inside surface. How much charge resides on the outer surface? (b) If the charge in part (a) is due to K+ ions (charge +e), how many such ions are present on the outer surface?
Three forces are applied to an object, as shown in the figure. Force F1→ has a magnitude of 21.3 newtons (21.3 N) and is directed 30.0∘ to the left of the +y axis. Force F2→ has a magnitude of 14.4 N and points along the +x axis. What must be the (a) magnitude and (b) direction (specified by the angle θ in the drawing) of the third force F3→ such that the vector sum of the three forces is 0 N? (a) Number Units (b) Number Units