Practice Problems: The Electric Field
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1. (easy) A small charge (q = 6.0 mC) is found in a uniform E-field (E = 2.9 N/C). Determine the force on the charge.

2. (easy) Find the electric field acting on a 2.0 C charge if an electrostatic force of 10500 N acts on the particle.

3. (easy) A dipole is set up with a charge magnitude of 2x10^-7 C for each charge (one is positive and the other is negative.) The distance between the charges is 0.15 m.  What are the magnitude and direction of the E-field at the midpoint of the dipole? (Assume the positive charge is on the left.) Also determine the force magnitude and direction for an electron at that position in the field.

4. (moderate) Two charges (q₁ and q₂) are located on the x axis on a coordinate system. They are both positive, but the second charge has twice the magnitude of the first. q₁ is at -0.5 m while q₂ is at +0.5 m. Determine the overall direction of the E-field at the various positions listed below:
A. At the origin
B. At x = 0 and y is negative
C. At x = -0.5 and y is positive
D. At x > 0 but x < +0.5 m and y = 0
E. At x > +0.5 m and y = 0
F. At x = +0.5 m and y > 0
Choose your answers from the following:
Choice 1: Along the +x-axis
Choice 2: Along the +y axis
Choice 3: Along the –x axis
Choice 4: Along the –y axis
Choice 5: Between 1 and 89 degrees from the +x axis
Choice 6: Between 91 and 179 degrees from the +x axis
Choice 7: Between 181 and 269 degrees from the +x axis
Choice 8: Between 271 and 359 degrees from the +x axis

5. (moderate) Repeat the previous question for points A,B,D and E, except assume that the first charge is positive and the second charge is negative.

6. (moderate) Charge q₁ (positive) is located at position (0, 0.5m) and has a magnitude of 2.9x10^-6 C. Charge q₂ (same as charge 1) is located at the origin. Assume that these charges are unable to move. A third charge (q₃ = 1.0x10^-9 C and m = 4.0x10^-25 kg) is located at (1.0 m, 0.25 m). Determine the force on and the acceleration of charge q₃ at this position, and describe the trajectory the third charge would take when released in the field caused by the other two charges.

7. (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.

8. (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 along the y direction (you decide whether the motion is along negative or positive y) 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.

9. (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.

Please supplement these problems with those found in your companion text.