homework_04_point_charge_and_charged_sphere

Point Charge and Charged Sphere

A point charge [q_1 = -8.5 \mu C] is located at the center of a thick conducting shell of inner radius [a = 2.8 cm] and outer radius [b = 4.1 cm], The conducting shell has a net charge of [q_2 = 2.1 \mu C].

1)

What is [E_x( P)], the value of the [x]-component of the electric field at point [P], located a distance [7.3 cm] along the [x]-axis from [q_1]?

• Given
  • [E = k \frac{ Q}{ r^2}]
    • Electric field of a point charge
• Let
  • [q_1 = -8.5 \mu C]
    • point charge at the center
  • [q_2 = 2.1 \mu C]
    • net charge of the conducting shell
  • [a = 2.8 cm = 0.028]
    • inner radius of the conducting shell
  • [b = 4.1 cm = 0.041 m]
    • outer radius of the conducting shell
  • [r = 7.3 cm = 0.073 m]
• [E_x( P) = k \left(\frac{ q_1 + q_2}{ r^2}\right) = -1.07968E7]

2)

What is [E_y( P)], the value of the [y]-component of the electric field at point [P], located a distance [7.3 cm] along the [x]-axis from [q_1]?

• [E_y( P)\ = 0]

3)

What is [E_x( R)], the value of the [x]-component of the electric field at point [R], located a distance [1.4 cm] along the [y]-axis from [q_1]?

• [E_x( R) = 0]

4)

What is [E_y( R)], the value of the [y]-component of the electric field at point [R], located a distance [1.4 cm] along the [y]-axis from [q_1]?

• Given
  • [E = k \frac{ Q}{ r^2}]
    • Electric field of a point charge
• Let
  • [q_1 = -8.5 \mu C]
    • point charge at the center
  • [q_2 = 2.1 \mu C]
    • net charge of the conducting shell
  • [a = 2.8 cm = 0.028]
    • inner radius of the conducting shell
  • [b = 4.1 cm = 0.041 m]
    • outer radius of the conducting shell
  • [r = 1.4 cm = 0.014 m]
• [E_x( P) = k \left(\frac{ q_1}{ r^2} \right) = -3.89872E8 ]