An important classical force law is called the Lorentz force and describes the force F acting on a point charge of mass m and charge q in the presence of an electric field E and/or a magnetic field B. It is given as: F =qE+qv x B where v is the velocity of the charged point mass. a. Consider the special case where q = 0 (i.e., the mass has no charge). What forces act on the mass? b. Now assume the particle charge q and at t = 0, with velocity Vo, it enters a region with uniform (i.e., constant) electric field E (but no B). Write an expression for the acceleration a the particle experiences in (Cartesian) component form. [Hint: Define a Cartesian coordinate system and assume the particle is at location r, when it enters the electric field.] c. Integrate this your answer to part b to determine a vector expression for the position of the particle r(t) (where r = a). [Hint: Break up into components if needed and treat each separately.] d. Now assume the particle charge q and at t = 0, with velocity Vo, it enters a region with uniform (i.e., constant) magnetic field B (but no E). Further, assume B points only along your chosen z-axis. Write an expression for the acceleration a the particle experiences in (Cartesian) component form. Solve this for r(t).

An important classical force law is called the Lorentz force and describes the force F acting on a point charge of mass m and charge q in the presence of an electric field E and/or a magnetic field B. It is given as: F =qE+qv x B where v is the velocity of the charged point mass. a. Consider the special case where q = 0 (i.e., the mass has no charge). What forces act on the mass? b. Now assume the particle charge q and at t = 0, with velocity Vo, it enters a region with uniform (i.e., constant) electric field E (but no B). Write an expression for the acceleration a the particle experiences in (Cartesian) component form. [Hint: Define a Cartesian coordinate system and assume the particle is at location r, when it enters the electric field.] c. Integrate this your answer to part b to determine a vector expression for the position of the particle r(t) (where r = a). [Hint: Break up into components if needed and treat each separately.] d. Now assume the particle charge q and at t = 0, with velocity Vo, it enters a region with uniform (i.e., constant) magnetic field B (but no E). Further, assume B points only along your chosen z-axis. Write an expression for the acceleration a the particle experiences in (Cartesian) component form. Solve this for r(t).

Similar questions

James (mass 81.0 kg) and Ramon (mass 57.0 kg) are 20.0 m apart on a frozen pond. Midway between them is a mug of their favorite beverage. They pull on the ends of a light rope stretched between them. Ramon pulls on the rope to give himself a speed of 1.10 m/s. What is James's speed? It must have the proper dimensions of speed.
In the earth's rest frame, two protons are moving away from each other at equal speed. In the frame of each proton, the other proton has a speed of 0.650c. Part A What does an observer in the rest frame of the earth measure for the speed of each proton? Express your answer as a multiple of the speed of light. V7 ΑΣΦ U = Submit Request Answer ?
You are the pilot of a spacecraft intended for travel at very high speeds. Before leaving you measure the spacecraft to be 31.4 m long and have a mass of 5.28 x 104 kg. During your travel, you pass a planet and exchange information with an observer on the planet. You are told that your spacecraft has been measured to be 28.6 m long. a. How fast is your spacecraft travelling with respect to the planet? b. You are told there is a nearby planet that is stationary with respect to the first planet. The observer on the first planet says it will take you 25 s to reach the nearby planet. How far away does your co-pilot on the spacecraft say the nearby planet is? c. How much energy was required to accelerate your spacecraft to this speed?
1. Two atomic clocks are synchronized. One is placed on a satellite, which orbits around the earth at high speed for a whole year. The other is placed in a lab and remains at rest, with respect to the earth. You may assume that both clocks can measure time accurately to many significant digits. a. Will the two clocks still be synchronized after one year? Explain your reasoning. b. Imagine that the speed of light was much slower than its actual value. How would the results of this experiment change if the speed of light was only twice the average speed of the satellite? Explain your reasoning, using a calculation.
Determine the magnitudes of all pin reactions for the frame loaded as shown. A Part 1 A₂ 350 mm B I 57⁰ 800 mm 27⁰ The Free-Body diagram for bar ABC is shown. Note that bar BD is a two-force member. Solve for the force BD. A, 780 N Answer: BD = 1 e Textbook and Media 57⁰ BD N Save for Later Using multiple attempts will impact your score. 10% score reduction after attempt 1 780 N Attempts: 0 of 3 used Submit Answer
dx 4x 3. In so-called "natural units" (which is just a sneaky way to let us ignore a bunch of constants), the relativistic kinetic energy of a rigid body is given by the formula 1 КЕ — т V1 – v2 where m is the rest mass of the body and v is its relative speed. Alien scientists on a space station are observing an object falling into a black hole. As the object falls, it is disintegrating, losing mass at a rate of 3 (so its mass is changing at a rate of -3). How fast is the kinetic energy of the main part of the object changing when its mass is 20, its velocity is .7, and it is accelerating at a rate of .1 (remember that acceleration is the derivative of velocity with respect to time: a = dt 1Note that this formula does not make sense when v > 1. That is because in natural units, a speed of 1 corresponds to the speed of light, and nothing with positive rest mass can go that fast.
q3
A frame B shown below in Figure 1, is rotated 90° about the z-axis, then translated 3 and 5 units relative to the n- and o-axis respectively, then rotated another 90° about the n-axis, and finally, 90° about the y-axis. Find the new location and orientation of the frame. (1,1,2) {B} F y a Figure 1 11
In the Earth reference frame, a 150-kg probe travels at 0.860c, while a 250-kg probe travels at 0.355c, in the opposite direction. Part A What is the speed of the 150-kg probe in the zero-momentum reference frame? V= Submit Part B 195) ΑΣΦ * Incorrect; Try Again; 2 attempts remaining V= Previous Answers Request Answer Submit What is the speed of the 250-kg probe in the zero-momentum reference frame? 15. ΑΣΦ ? Previous Answers Request Answer Co ? Co
R3B2. Alicia is a student on a passenger train moving at a constant velocity relative to the ground. She synchronizes her watch with the station clock as she passes through the town of Bannon station, and then compares her watch with the station clock as she passes through the Center town station farther down the line. The ground is an inertial frame, and the Bannon and Center clocks are synchronized in that frame. (1) Using a model or diagram, is the time she measures between the events of passing through these towns a proper time? (2) Is it a coordinate time in some inertial reference frame? (3) Is it the spacetime interval between the events?