An object with a charge of -4.4 uC and a mass of 1.4×10^−2 kg experiences an upward electric force, due to a uniform electric field, equal in magnitude to its weight.

Find the magnitude of the electric field. Find the direction of the electric field.
If the the electric charge on the object is doubled while the mass remains the same, find the direction and magnitude of its acceleration.
If the electric charge on the object is doubled while its mass remains the same, find the direction and magnitude of its acceleration

To find the magnitude of the electric field, we can use the equation:

Electric Force (F) = Charge (Q) * Electric Field (E)

In this case, the electric force is equal in magnitude to the weight of the object, which is given by:

Weight (W) = mass (m) * gravitational acceleration (g)

Step 1: Calculate the weight of the object.
W = m * g

Given: m = 1.4×10^−2 kg (mass of the object)
g = 9.8 m/s^2 (standard gravitational acceleration)

W = (1.4×10^−2 kg) * (9.8 m/s^2)

Step 2: Equate the weight with the electric force.
W = F

Step 3: Set up the equation using the defined quantities.
F = Q * E

Step 4: Solve for E.
E = F / Q

Given: Q = -4.4 uC (charge of the object, -4.4 * 10^-6 C)

E = (W) / (Q)
E = (1.4×10^−2 kg * 9.8 m/s^2) / (-4.4 * 10^-6 C)

Calculate the magnitude of the electric field using the given values.

To find the direction of the electric field, we need to determine whether it is pointing upward or downward. In this problem, the object experiences an upward electric force equal in magnitude to its weight. Therefore, the direction of the electric field is upward.

If the electric charge on the object is doubled while the mass remains the same, the magnitude of the force experienced by the object will change. We can find the magnitude of its acceleration using Newton's second law:

Force (F) = mass (m) * acceleration (a)

Given that the mass remains the same and the charge doubles, the new force experienced by the object is:

New force (F_new) = (2 * Q) * E

Step 1: Calculate the new force by substituting the given values.
F_new = (2 * -4.4 * 10^-6 C) * E

Step 2: Use Newton's second law to find the magnitude of acceleration.
F_new = m * a, where m is the mass given and a is the acceleration.

Substituting the values, we get:
(2 * -4.4 * 10^-6 C) * E = m * a

Divide both sides by m to get:
(2 * -4.4 * 10^-6 C * E) / m = a

The magnitude of acceleration can be determined by evaluating the right side of the equation using the given values and the previously calculated magnitude of the electric field.

The direction of acceleration for the object will depend on the direction of the electric field. Considering that the electric field is upward, the acceleration will be in the same direction as the electric field.

If the electric charge on the object is doubled while the mass remains the same, the magnitude of its acceleration will be determined by evaluating the right side of the equation above using the given values and the previously calculated magnitude of the electric field. The direction of the acceleration will remain the same as the electric field (upward in this case).