Physics Problems

1. A particle (charge = +40 µC) is located on the x axis at the point x = –20 cm, and a second particle (charge = –50 µC) is placed on the x axis at x = +30 cm. What is the magnitude of the total electrostatic force on a third particle (charge = –4.0 µC) placed at the origin (x = 0)? 56 N

2. Each of two small non-conducting spheres is charged positively, the combined charge being 40 µC. If each sphere is repelled from the other by a force having a magnitude of 2.0 N when the two spheres are 50 cm apart, determine the charge on the sphere having the smaller charge. 1.4 µC

3. A charge of +80 µC is placed on the x axis at x = 0. A second charge of –50 µC is placed on the x axis at x = 50 cm. What is the magnitude of the electrostatic force on a third charge of 4.0 µC placed on the x axis at x = 30 cm? 77 N

4. A particle (m = 50 g, q = 5.0 µC) is released from rest when it is 50 cm from a second particle (Q = –20 µC). Determine the magnitude of the initial acceleration of the 50-g particle. 72 m/s²

5. Three point charges, two positive and one negative, each having a magnitude of 20 µC are placed at the vertices of an equilateral triangle (30 cm on a side). What is the magnitude of the electrostatic force on the negative charge? 69 N

6. Three point charges, two positive and one negative, each having a magnitude of 20 µC are placed at the vertices of an equilateral triangle (30 cm on a side). What is the magnitude of the electrostatic force on one of the positive charges? 40 N

7. Identical point charges Q are placed at each of the four corners of a 3.0 m x 4.0 m rectangle. If Q = 40 µC, what is the magnitude of the electrostatic force on any one of the charges? 2.4 N

8. A +15-nC point charge is placed on the x axis at x = 1.5 m, and a –20-nC charge is placed on the y axis at y = –2.0m. What is the magnitude of the electric field at the origin? 75 N/C

9. A 40-µC charge is positioned on the x axis at x = 4.0 cm. To produce a net electric field of zero at the origin where should a –60-µC charge be placed? 4.9 cm

10. In the diagram shown below, determine the resultant electric field (magnitude & direction) at point P due to the three charges shown. E = 7.2 x 10⁷ n/c @ 95.5^o

11. A particle (mass = 4.0 g, charge = 80 mC) moves in a region of space where the electric field is uniform and is given by E_x = –2.5 N/C, E_y = E_z = 0. If the velocity of the particle at t = 0 is given by v_x = 80 m/s, v_y = v_z = 0, what is the speed of the particle at t = 2.0 s? 20 m/s

12. A particle (mass = 5.0 g, charge = 40 mC) moves in a region of space where the electric field is uniform and is given by E_x = 2.5 N/C, E_y = E_z = 0. If the velocity of the particle at t = 0 is given by v_y = 50 m/s, v_x = v_z = 0, what is the speed of the particle at t = 2.0 s? 64 m/s

13. A charge of 50 µC is placed on the y axis at y = 3.0 cm and a 77-µC charge is placed on the x axis at x = 4.0 cm. If both charges are held fixed, what is the magnitude of the initial acceleration of an electron released from rest at the origin? 1.2 x 10²⁰ m/s²

14. The electron gun in a television tube is to accelerate electrons (mass 9.1 x 10^–31 kg, charge 1.6 x 10^–19 C) from rest to 3.0 x 10⁷ m/s within a distance of 2.0 cm. What electric field is required? 128,000 N/C

15. A proton moving at 3 x 10⁴ m/s is projected at an angle of 30° above a horizontal plane. If an electric field of 400 N/C is acting down, how long does it take the proton to return to the horizontal plane? (Ignore gravity) [m_proton = 1.67 x 10^–27 kg, q_proton = +1.6 x 10^–19 C] 7.8 x 10^-7 sec

16. An edge-on view of two very large charged parallel plates is shown in the left hand diagram below.

· If the total charge density on each plate is 20 uC/m², determine the Electric Field between the plates. 2.26 x 10⁶ n/c

· If a positive 5 uC charge is placed next to the positive plate, determine the force on the charge. 11.3 n

· Determine the velocity of the 5 uC charge when it reaches the negative plate. 23.7 m/s

· The separation of the plates is 10 cm, and the mass of the charge is 4 grams.

1. Two charged thin spherical shells are shown in right hand diagram below. Q1 = + 50 uC, Q2 = - 80 uC, R1 = 20 cm, R2 = 40 cm.

· Determine the Resultant Electric Field at R =10 cm, R =30 cm, & R = 50 cm. (0, 5 x 10⁶ n/c, -1.08 x 10⁶ n/c)

· Determine the Electric Potential at R =10 cm, R =30 cm, & R = 50 cm. (450,000 V, -300,000 V, -540,000 V)

1. An edge on view of three very large (infinite) sheets of charge are shown below. Sheet 1 has a surface charge density of +2 uC/m² , Sheet 2 has a charge density of -4 uC/m² , Sheet 3 has a charge density of +6 uC/m².

· Determine the resultant electric field due to all three sheets: To the left of sheet 1.; Between sheet 1 & 2.; Between sheet 2 & 3.; the right of sheet 2. ( -2.26 x 10⁵ n/c, 0, -4.52 x 10⁵ n/c, +2.26 x 10⁵ n/c)

· Determine the potential difference between point A in the exact middle between sheet 1 & 2, and point B in the exact middle between sheet 2 & 3. (4.52 x 10⁴ Volts)