Practice Problems: Motion of a Charged Particle in an E-field
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1. (easy) An electron is released (from rest) in a uniform E-field with a magnitude of 1.5x103N/C. Determine the acceleration of the electron due to the E-field.
2. (easy) A single proton is accelerated in a uniform E-field (directed eastward) at 3.2x108 m/s2. Find the magnitude of the field and direction of the acceleration.
3. (moderate) Two charged particles, one (with a charge of +2μC and a mass m) located on the origin of an axis system and a second (with a charge of +3μC and a mass of 2m) located at x = 1 m are exerting a force on each other. Determine the magnitude of the force and then describe the trajectory each particle will undergo, including their velocities and accelerations.
4. (moderate) A charged particle (-3.0C with a mass of 0.0002 kg) is injected into an E-field with an initial speed of 2000 m/s along the +z axis. The E-field is uniform in this region (500 N/C), and directed in the +y direction. Determine the acceleration components for all three directions (x,y, and z). Additionally, calculate the length of time needed to the particle to move 1x108 m in the -y direction and the distance moved along the other two axes over that time frame. Assume that the initial position of the particle is at the origin of the axis system.
5. (moderate) Charge q1 (positive) is located at position (0, 0.50 m) and has a magnitude of 2.9x10-6 C. Charge q2 is located at the origin. Assume that these charges are identical and unable to move. A third charge (q3 = +1.0x10-9 C and m = 4.0x10-25 kg) is located at (1.00 m, 0.25 m). Determine the force on and the acceleration of the charge in this position, and describe the trajectory the third charge would take when released in the field caused by the other two charges.
6. (moderate) Based on the information shown in the sketch below, determine the trajectory of the positively charged particle as it enters into the E-fields shown. 