A 0.10 g plastic bead is charged by the addition of 1.0 x 1010 excess electrons. What electric field (strength and direction) will cause the bead to hang suspended in the air?

To determine the electric field required for the plastic bead to hang suspended in the air, we can calculate it using the following steps:

Step 1: Calculate the charge on the plastic bead.
The charge on an electron is -1.6 x 10^-19 C. Therefore, the total charge added to the plastic bead can be calculated as follows:
Total charge = Number of excess electrons x Charge of 1 electron
Total charge = (1.0 x 10^10) x (-1.6 x 10^-19 C)
Total charge = -1.6 x 10^-9 C

Step 2: Calculate the weight of the plastic bead.
The weight of an object is given by the equation:
Weight = mass x acceleration due to gravity
Weight = (0.10 g) x (9.8 m/s^2)
Weight = 0.98 x 10^-3 N

Step 3: Calculate the electric field strength required for the bead to hang suspended.
The electric force between the charged bead and an external electric field will have the same magnitude as the weight of the bead acting downwards, but in the opposite direction. The equation for electric force is given by:
Electric force = Electric field strength x Charge

Since the bead needs to hang suspended, the electric force should balance the weight of the bead. Therefore:
Electric force = Weight

Hence, we can write the equation as:
Electric field strength x Charge = Weight

Substituting the known values:
Electric field strength x (-1.6 x 10^-9 C) = 0.98 x 10^-3 N

Solving for the electric field strength:
Electric field strength = (0.98 x 10^-3 N) / (-1.6 x 10^-9 C)

Calculating this:
Electric field strength ≈ -6.13 x 10^5 N/C

Therefore, the required electric field strength for the bead to hang suspended in the air is approximately 6.13 x 10^5 N/C, directed upwards.

To determine the electric field required for the bead to hang suspended in the air, we need to consider the balance of gravitational force and electric force on the bead.

First, we need to determine the charge on the plastic bead. Since each electron has a charge of -1.6 x 10^-19 coulombs, and there are 1.0 x 10^10 excess electrons added to the bead, the total charge on the bead is:

Charge on the bead = (1.0 x 10^10 electrons) * (-1.6 x 10^-19 C/electron)
= -1.6 x 10^-9 C

Next, we need to calculate the mass of the plastic bead. Given that the mass of the bead is 0.10 g, we convert it to kilograms:

Mass of the bead = 0.10 g * (1 kg / 1000 g)
= 0.0001 kg

Now, we can calculate the gravitational force acting on the bead due to gravity. The force on the bead can be determined using the following formula:

Force due to gravity = mass * gravitational acceleration

Considering the acceleration due to gravity is 9.8 m/s^2:

Force due to gravity = 0.0001 kg * 9.8 m/s^2
= 9.8 x 10^-4 N

Since the bead is in equilibrium, the electric force on the bead should cancel out the gravitational force.

The electric force is given by the formula:

Electric force = charge * electric field

Rearranging the formula, we find:

Electric field = Electric force / charge

Thus, the formula to calculate the electric field required for the bead to hang suspended in the air is:

Electric field = (9.8 x 10^-4 N) / (-1.6 x 10^-9 C)

Evaluating this calculation gives us the electric field:

Electric field = -6.125 x 10^5 N/C

The negative sign indicates that the electric field is directed opposite to the direction of the gravitational force, meaning it should be pointing upwards.

Therefore, the electric field required for the bead to hang suspended in the air is approximately -6.125 x 10^5 N/C in the upward direction.

The charge is Q = -10^10*e

e is the electron charge, 1.6*10^-19 C

You need an electric field pointed down to balance the weight of the drop. The strength of the field is given by
E*Q = M*g

E = M*g/Q newtons/coulomb