A particle of charge q and mass m is subjected to an electric field E = E0 (1 – ax2) in the x-direction, where a and E0 are constants. Initially the particle was at rest at x =0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is:

19.9 Particle 1 has a mass of m₁ = 4.00 × 10 6 kg, while particle 2 has a mass of m₂ = 7.00 × 106 kg. Each has the same electric charge. These particles are initially held at rest, and the two-particle system has an initial electric potential energy of 0.150 J. Suddenly, the particles are released and fly apart because of the repulsive electric force that acts on each one (see the figure). The effects of the gravitational force are negligible, and no other forces act on the particles. At one instant following the release, the speed of particle 1 is measured to be v₁ =172 m/s. What is the electric potential energy at this instant? ulf Number i 9 my 9 9 m1 m2 (a) Initial (at rest) (b) Final 9 m2 Units v2f <

True of false ? The stopping power is a function of the charge of the particle, energy of the particle, and shape of the medium.

A negatively charged particle of mass 8.0 x 10-13 kg is traveling rightward between two plates separated by a distance d = 50 cm, as shown below. The particle is launched with a speed of 1.0 x 104 m/s at the left plate, and strikes the right plate at a speed of 5.0 x 10³ m/s. The left plate is at electric potential V₁ = +1.0 V, while the right plate is at electric potential V₂ = -5.0 V. Assume the electric field between the plates is uniform, and ignore the effect of gravity. 2 (a) (b) V₁ d 7 V₂ Does the potential energy of the particle increase or decrease as it moves from the left plate to the right plate? Is the electric field between the plates directed rightward or leftward? Justify your answers briefly. Show clearly that the electric field between the plates has magnitude 12 V/m (or 12 N/C). Then find the charge of the particle (with correct magnitude and sign). (Note: You may obtain the charge using either energy considerations or a "force and kinematics" approach.

Hi, can anyone solve this with a detailed explanation.   The electron in a hydrogen atom is initially at a distance 2.12 Å from the proton, and then moves to a distance 0.529 Å from the proton. (a) Calculate the change in the force between the proton and the electron. (b) Calculate the change in the potential energy between the proton and the electron. (c) Calculate the change in the velocity of the electron.

1. Two persons were practicing social distancing to alleviate the spread of COVID-19. Social distancing requires a minimum of 3 feet distance from person to person. However, due to their eagerness to share some rumors, the two persons decided to approach each other and now within the intimate distance (12 inches). If person A weighs 60 kg. and person B weighs 68 kg, determine the work done for this act. Take G = 6.67408 x 10-11 m³ kg¬'s-2. A. 6.8076 ergs B. 8.0766 ergs C. 5.9559 ergs D. 5.5599 ergs 2. Find the moment of mass from the x-axis for y = x In(x) – 3x and y = 1 bounded by x = 3 and x = 6. The surface density is equal to 0.37 kg/units'. A. 24.0793 kg. В. -38.6209 kg C. 27.8043 kg. D. -36.8902 kg. 3. In 2019, SCUBA divers from Mexico explores the Atlantic Ocean (64 lb/ft) and finds a circular clock thought to be the ancient remnants of the legendary Atlantis. If the clock measures 1.3 ft. in diameter and depth is measured to be 1250 ft. from the surface to the center of this…

The figure below shows a small, charged sphere, with a charge of q = +38.0 nC, that moves a distance of d = 0.171 m from point Ato point B in the presence of a uniform electric field E of magnitude 280 N/C, pointing right.   (a) What is the magnitude (in N) and direction of the electric force on the sphere? magnitude n?   (b) What is the work (in J) done on the sphere by the electric force as it moves from A to B?   J??   (C) What is the change of the electric potential energy (in J) as the sphere moves from A to B? (The system consists of the sphere and all its surroundings.)   PEB − PEA =  ?  J   (D)What is the potential difference (in V) between A and B? VB − VA = ? V

The figure below shows a small, charged sphere, with a charge of q = +41.0 nC, that moves a distance of d = 0.177 m from point A to point B in the presence of a uniform electric field E of magnitude 265 N/C, pointing right.   (a) What is the magnitude (in N) and direction of the electric force on the sphere?     (b) What is the work (in J) done on the sphere by the electric force as it moves from A to B?     (c) What is the change of the electric potential energy (in J) as the sphere moves from A to B? (The system consists of the sphere and all its surroundings.)     (d) What is the potential difference (in V) between A and B?

A 8 kg particle is in a potential given by U(x) = 1 x^4 - 7 x^2 - 3 x + 8 (J).  Calculate the acceleration of the particle when it is at x = 1 m, in m/s2. (Please answer to the fourth decimal place - i.e 14.3225)

A square of side a = 1 m has charges +Q and -Q (Q = 2 μC) alternating from one corner tothe next. Find the electric potential energy for the systems of charges.