(0, 0,0) and the 5. The point o is the origin of the coordinate system, o = coordinates of b are b = (x,y, z). The electric potential at o is zero, V. = 0. Hence, the electric potential at b is V = - SE· dr. You can take any path from o to b. (a) Here is one particular path from o to b. First move on a straight line from o to a = (x,0,0), then from a to a' (x, y, 0), and finally from a' to b = (x, y, z). Make a plot of this path, indicating the coordinate system and the locations of a, a' and b. – sE · dr depends only on the y However, the line integral V coordinate of b = (x, y, z). Hence, in the following, we will focus on b = (0, y, 0) and take the straight path from o to b. (b) Compute E · dr for y < 0. (c) Compute sE · dr for 0 < y < d. What is the value of the electric pontential at b = (0, d, 0)?

A thin rod has uniform charge per length 3w over its length H. The distance between point A and point B is 3H and the distance between point A and point P is 2H. We introduce an integration variables with 5 = 0 chosen to be at point A and the +s direction to be down. The small red segment has length ds and charge dg. We want to find the electric potential at point P. Draw it out--label the all the lengths and the integration variable! A. dV= B. dV C. dV = D. dV= A Which expression below gives the voltage d'V from the small charge dg in the small segment ds? Choose from the choices (A thru F) below: E. dV= F. dV= B с Kdq √√²+4H² Kdg (s² +4H²) Kdq 5 Kdq √(8+3H)² +4H² Kdg ((s+3H)² +4H²) 3.Kdq H ((8+6H)² +97²)³/2 -P +y >+x What are the limits of integration s? [Select] [Select]

1.  How do you find the gravitational potential of two masses for any position around them that is outside the masses?  Specifically, take the Earth and the Moon as an example.  We need big masses like these because G is so small.  Gravity is very weak.  When we do electricity, we can work with smaller amounts of matter and smaller distances because electrical forces are stronger than gravitational forces.  Here are the numbers https://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html   MEarth = 5.97 × 1024 kg   (Mass of Earth) MMoon = 7.35 × 1022 kg     (mass of Moon) RE-M = 3.85 × 108 m    (average separation of Earth and Moon centers) REarth = 6.378 × 106 m  (radius of Earth) RMoon = 1.738 × 106 m  (radius of Moon)

Find the force vector F on an object of mass m the uniform gravitational field when it is at height z = 0. The +z direction is up. Express vector force in terms of m, z. g. and k, where k is the unit vector in the +z direction. To create the k character: In the equation editor window, select "More", then select "Vectors", and you will find what you need. To write out a vector: for example, if the answer has both x and y components, you would answer in the format Fi + Fj F(z) = -mgk Now find the gravitational potential energy U(z) of the object when it is at an arbitrary height z. Take zero potential to be at position z=0. Keep in mind that the potential energy is a scalar, not a vector. Express U(z) in terms of m. z. and g. U(2)= In what direction does the object accelerate when released with initial velocity upward? downward Oupward or downward depending on the initial mass m. upward or downward depending on the initial velocity upward Now consider the analogous case of a particle…