Question

1. Three point charges, qi, q2, and qa carry same amount of charge, +Q each, are located on x-axis in a vacuum. Their coordinate are (1,1), (3,1), and Find the resultant force acting on each of the point charges in term of Q. 2. Four point charges are placed at the corner of a square plate. q1, q2, and q3 are positively charged particles and e is an electron. Find the resultant force acting on q3 if the area of the square plate is 25 cm2 3. Estimate the distance between the electron of a Helium atom to the nucleus if 28 MeV is needed to remove it from the atom. [Given that there are 2protons, 2 neutrons and 2 electrons in an Helium atom) 4. point charges P, Q, R are placed on the same axis. Distances between P-Q and P-R are r cm and 10 cm respectively. Determine the position of Q where the resultant force acting on Q is 0N R 100 nC 5. Two identical conducting spheres hang from a light-weight string carry 10 nC of charges each maintain equilibrium state at a distance of 5 mm from each other while making 8-10o from the vertical line. Find the weight of the spheres. 5 mm

Answer 1

Each charge carry same amount of charge + Q Let's calculate net force on q, Force on q_1 due to q_2 (F_^rightarrow_q_1, q_3) = 1/4 pi epsilon_0 [r = 6m] = 9 times 10^9/6 Q^2 = (1.5 times 10^9)Q^2 Net Force on q_3 = F^rightarrow_q_1, q_2 + F^rightarrow_q_1, q_3 = (3.75 times 10^9)cs^2 N [toward left] Now, let's calculate net force on q_2 F_q_2, q_3 leftrightarrow F_q_2, q_1 (q_2) Magnitude of force on q_2 due to q_1 = F^rightarrow_q_1, q_2 [F^rightarrow_q_1, q_2 = (2.25 u^9)Q^2] F^rightarrow_q_2, q_1 = (2.25 times 10^9)Q^2 Magnitude of force on q_2 due to q_3 = 1/4 pi epsilon_0 q_2q_3/r^2 [r = 4m] = (9 times 10^9)Q^2/16 = (0.5625 times 10^9)Q^2 Net Force = F^rightarrow_q_2, q_1 - F^rightarrow_q_2, q_3 = [(2.25 - 0.5625) times 10^9]Q^2 N = [1.6875 times 10^9]Q^2 N [towards right] finally, Net Force on q_3 rightarrow^F_q_3, q_2 F_q_3, q_1 Magnitude of Force on q_3 due to q_1 = (1.5 times 10^9)Q^2 N