Biologists use optical tweezers to manipulate micron-sized objects using a beam of light. In this technique, a laser beam is focused to a very small-diameter spot. Because small particles are attracted to regions of high light intensity, the focused beam can be used to "grab" onto particles and manipulate them for various experiments. In one experiment, a 10 mW laser beam is focused to a spot that has a diameter of 0.62 μm. a. What is the intensity of the light in this spot?
b. What is the amplitude of the electric field?

In a thunderstorm, charge builds up on the water droplets or ice crystals in a cloud. thus, the charge can be considered to be distributed uniformly throughout the cloud. for the purposes of this problem, take the cloud to be a sphere of diameter 1.00 kilometer. the point of this problem is to estimate the maximum amount of charge that this cloud can contain, assuming that the charge builds up until the electric field at the surface of the cloud reaches the value at which the surrounding air breaks down. this breakdown means that the air becomes highly ionized, enabling it to conduct the charge from the cloud to the ground or another nearby cloud. the ionized air will then emit light due to the recombination of the electrons and atoms to form excited molecules that radiate light. in addition, the large current will heat up the air, resulting in its rapid expansion. these two phenomena account for the appearance of lightning and the sound of thunder. take the breakdown electric field of air to be eb=3.00ă—106n/c. part a estimate the total charge q on the cloud when the breakdown of the surrounding air is reached. express your answer numerically, to three significant figures, using ďµ0=8.85ă—10â’12c2/(nâ‹…m2) .

Africtionless piston-cylinder contains 50 l of saturated liquid r-134a. the piston has a mass and an area resulting in an applied pressure of 500 kpa on the refrigerant. the refrigerant is now heated until its temperature rises to 70∘c. calculate the work (in kj) done during this process.

Automobile fuel efficiency is often measured in miles that the car can be driven per gallon of fuel (mpg). heavier cars tend to have lower fuel efficiencies (lower mpg ratings). which variable (weight or fuel efficiency) is most naturally considered the explanatory (predictor) variable in this context?