Electric charge can accumulate on an airplane in flight. you may have observed needle-shaped metal extensions on the wing tips and tail of an airplane. their purpose is to allow charge to leak off before much of it accumulates. the electric field around the needle is much larger than the field around the body of the airplane and can become large enough to produce dielectric breakdown of the air, discharging the airplane. to model this process, assume that two charged spherical conductors are connected by a long conducting wire and a charge of 65.0 µc is placed on the combination. one sphere, representing the body of the airplane, has a radius of 6.00 m, and the other, representing the tip of the needle, has a radius of 2.00 cm. (a) what is the electric potential of eachsphere?

An alligator swims to the left with a constant velocity of 5 \,\dfrac{\text{m}}{\text s}5 s m ? 5, space, start fraction, m, divided by, s, end fraction. when the alligator sees a bird straight ahead, the alligator speeds up with a constant acceleration of 3 \,\dfrac{\text {m}}{\text s^2}3 s 2 m ? 3, space, start fraction, m, divided by, s, start superscript, 2, end superscript, end fraction leftward until it reaches a final velocity of 35 \,\dfrac{\text {m}}{\text s}35 s m ? 35, space, start fraction, m, divided by, s, end fraction leftward. how many seconds does it take the alligator to speed up from 5 \,\dfrac{\text {m}}{\text s}5 s m ? 5, space, start fraction, m, divided by, s, end fraction to 35 \,\dfrac{\text {m}}{\text s}35 s m ? 35, space, start fraction, m, divided by, s, end fraction?

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Aparticle of mass m is placed in a one-dimensional box of length l. the box is so small that the particle’s motion is relativistic, so that e p2/2m is not valid. (a) derive an expression for the energy levels of the particle using the relativistic energy–momentum relation and the quantization of momentum that derives from connement. (b) if the particle is an electron in a box of length l 1.00 1012 m, nd its lowest possible kinetic energy. by what percent is the nonrelativistic formula for the energy in error?