1. A conducting ball with a radius of 10 cm has an electric charge of 500 μC. Points A, B, and C lie in line with the center of the ball at a distance of 12 cm, 10 cm and 8 cm respectively from the center of the ball. Calculate the electric field strength at points A, B, and C!

__Known____:__

The radius of the conducting ball (R) = 10 cm = 0.1 m

Electric charge (q) = 500 μC = 500 x 10^{-6} C

r_{A} = 12 cm = 0,12 m

r_{B} = 10 cm = 0,1 m

r_{C} = 8 cm = 0,08 m

Coulomb constant (k) = 9 x 10^{9}

__Wanted:__ The electric field strength at point A (E_{A}), at point B (E_{B}) and at point C (E_{C})

__Solution:__

a) The electric field strength at point A

E_{A} = k q / r_{A}^{2} = (9 x 10^{9})(500 x 10^{-6}) / (0,12)^{2} = (4500 x 10^{3}) / 0,0144 = 312500 x 10^{3} = 3,125 x 10^{8 }N/C

b) The electric field strength at point B

E_{B} = k q / r_{B}^{2} = (9 x 10^{9})(500 x 10^{-6}) / (0,1)^{2} = (4500 x 10^{3}) / 0,01 = 450.000 x 10^{3} = 4,5 x 10^{8 }N/C

c) The electric field strength at point C

E_{C} = 0 for being in the ball.

2. If a test charge of 4 nC is placed at a point, the charge experiences a force of 5 × 10 – 4 N. What is the magnitude of the electric field E at that point?

__Known:__

Test electric charge (q) = 4 nC = 4 x 10^{-9} Coulomb

Electric force (F) = 5 × 10^{-4} N

__Wanted:__ The magnitude of the electric field (E)

__Solution:__

E = F / q = (5 × 10^{-4}) / (4 x 10^{-9}) = 1,25 x 10^{5 }N/C

3. Two charges q_{B} = 12 μC and q_{C} = 9 μC are placed at the vertices of a right triangle as in Fig. Determine the electric field strength felt at point A!

__Known:__

Charge at point B (qB) = 12 μC = 12 x 10^{-6} C

Charge at point C (qC) = 9 μC = 9 x 10^{-6} C

Coulomb constant (k) = 9 x 10^{9}

r_{AC} = 4 cm = 0,04 m

r_{AB} = 3 cm = 0,03 m

__Wanted:__ electric field strength at point A

__Solution:__

E_{AC} = k q / r^{2} = (9 x 10^{9})(9 x 10^{-6}) / (0,04)^{2} = 81 x 10^{3} / 0,0016 = 5,0 x 10^{7} N/C

E_{AB} = k q / r^{2} = (9 x 10^{9})(9 x 10^{-6}) / (0,03)^{2} = 81 x 10^{3} / 0,0009 = 9,0 x 10^{7} N/C