I need immediate help on these questions:.

2.a small plastic ball with a mass of 0.005kg is suspended from a thread and hangs in equilibrium as shown in the drawing below when a small rod with a 2 uC charge is brought to within 3mm of the ball
a)find the tension force in the string
b) find the charge on the plastic ball(including sign)

3.A parallel plate capacitor has a potential difference of 100 volts and a distance between plates of 1cm. A small charged particle with a mass of 2grams is suspended in mid-air between the plates
a)find the electrostatic force acting on the particle(including direction)
b) find the electric charge that exists on the particle(including the sign)

Please!!! Including explanation and answer!

For both questions, we will need to apply the principles of electrostatics.

Question 2:
a) To find the tension force in the string, we need to consider the gravitational force acting on the plastic ball and the electrostatic force between the ball and the charged rod.

First, we calculate the gravitational force. The weight of an object can be determined using the formula F = mg, where F is the force, m is the mass, and g is the acceleration due to gravity. In this case, the weight is given by F_gravity = (0.005 kg) * (9.8 m/s^2) = 0.049 N.

Next, we need to calculate the electrostatic force between the ball and the rod. The formula for electrostatic force is given by F_electrostatic = k * (|q1| * |q2|) / r^2, where k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between the charges. In this case, q1 = 2 uC (which can be converted to 2 * 10^-6 C), q2 = charge on the plastic ball, and r = 3 mm (which can be converted to 3 * 10^-3 m).

Since the system is in equilibrium, the tension force in the string is equal to the sum of the gravitational and electrostatic forces. Therefore, Tension = F_gravity + F_electrostatic.

b) To find the charge on the plastic ball, we can rearrange the electrostatic force formula. We know that F_electrostatic = k * (|q1| * |q2|) / r^2, so we can rearrange it as q2 = (F_electrostatic * r^2) / (k * |q1|).

Question 3:
a) To find the electrostatic force acting on the small charged particle, we can use the formula F_electrostatic = q * E, where q is the charge on the particle and E is the electric field strength between the plates. The electric field strength (E) can be calculated using the formula E = V / d, where V is the potential difference and d is the distance between the plates.

b) To determine the electric charge on the particle, we can use the formula q = m * g / E, where m is the mass of the particle, g is the acceleration due to gravity, and E is the electric field strength.

Please note that to obtain the numerical answers, you will need to substitute the given values into the equations and perform the calculations.