m-0.5kg R-0. 15m>>radius of ball a. h-? So the ball just to leave the trail at...
2 BALL AND PLANE Consider a spherical shell of radius R and charge per unit area σ1 sitting at the origin. There is also an infinie plane parallel to the x- y plane sitting at z-zo with charge per unit area Oz. We will take Zo > R. Compute the electric field at the following locations: 2.1 10 POINTS The origin. 2.2 15 POINTS The point (xo,0,0) with xo> R 2.3 15 POINTS The point (X1, 0,21) with 0 <...
A hollow ball with radius R- 2 cm has a charge of -2 nC spread uniformly over its surface (see the figure). The center of the ball is at Pt --3, o, 0> cm. A point charge of 5 nC is located at Ps-<3, 0, 0> cm. (The diagram below is not drawn exactly to scale) Р, Х P3 . What is the net electric field at location P2-0,5, 0 cm? x N/C At a particular instant an electron is...
A cylindrical reservoir with a radius R is hang on a string (so it may freely rotate). The reservoir has two nozzles at its bottom part. The nozzles are oriented tangentially to the reservoir surface. They exert thus a torque giving rise to rotations about the vertical axis. Find the angular velocity of the reservoir rotation. Assume that the reservoir radius is much larger than that of the nozzles. The separation between the nozzles is 2L R>r Figure 1: water...
Problem 2 A ball of radius b and mass M is rolling without slipping on the surface of a ring of radius R > b. The angular speed of the ball is w. Suppose the ring is rotating with angular speed 12 as shown in the figure and the ball is rolling without slipping. What is the speed of the center of mass of the ball? Write your answer using some or all of the following: b, R, w and...
Problem 2 A ball of radius b and mass M is rolling without slipping on the surface of a ring of radius R > b. The angular speed of the ball is w. Suppose the ring is rotating with angular speed 12 as shown in the figure and the ball is rolling without slipping. What is the speed of the center of mass of the ball? Write your answer using some or all of the following: b, R, w and...
2.1 2.2 2.3 2 BALL AND PLANE Consider a spherical shell of radius R and charge per unit area ơi sitting at the origin. There is also an infinite plane parallel to the x - y plane sitting at zzo with charge per unit area σ2. We will take z02R. Compute the electric field at the following locations: 2.1 10 POINTS The origin. 2.2 15 POINTS The point (xo.0,0) with xo>R 2.3 15 POINTS The point (x1,0, z) with 0...
Problem 13.50 A hollow ball with radius drawn exactly to scale.) = 2 cm has a charge of 2 nC spread uniformly over its surface see the figure). The center of the ball is at P1-く2, 0 o» cm. A point charge of 3 nC is located at P3 =c? o o> cm. The diagram below is not PIX Ps. What is the net electric field at location P2 -0,7,cm N/C At a particular instant an electron is at location...
4. Let {Sn,n > 0} be a symmetric Random Walk on Z. with So-0. Defined Y, max{Sk, 1 3 k S nt, for n 2 0, prove, thanks to a counterexample, that Y is not a Markov Chain
1. A hollow conducting sphere of radius R has a charge Q placed on its surface. A point charge Q1 is placed at a distance d> R from the center of the sphere. a) Using the method of superposition, find a combination of two image charges inside the sphere that result in the correct electric field and potential outside the sphere. b) What is the force between the sphere and the point charge? What is the force whern 0, and...
Problem 4. A solid sphere of mass m and radius r rolls without slipping along the track shown below. It starts from rest with the lowest point of the sphere at height h 3R above the bottom of the loop of radius R, much larger than r. Point P is on the track and it is R above the bottom of the loop. The moment of inertia of the ball about an axis through its center is I-2/S mr. The...