A tiny ball of mass 0.60g is suspended from a rigid support with a piece of thread in a horizontal field of intensity 700N/C.The ball is in equilbrum when the thread is inclined at an angle of 20^(0) to the vertical.What are the magnitude and sign of the charge on the ball?take g=9.8m/s-2 (a)(-)0.0000031C (b)0.0000032C(c)0.0000042C(d)(-)0.0041C
0041
Solution
To find the magnitude and sign of the charge on the ball, we need to use the concept of electrostatic equilibrium. In this case, the gravitational force acting downwards on the ball is balanced by the electrostatic force acting upwards on it due to the electric field.
First, let's consider the gravitational force on the ball. The formula for the gravitational force (F_g) acting on an object is given by:
F_g = m * g
where m is the mass of the object and g is the acceleration due to gravity (9.8 m/s^2).
In this case, the mass of the ball (m) is 0.60 g, but we need to convert it to kg:
m = 0.60 g = 0.60 * 10^(-3) kg (since 1 g = 10^(-3) kg)
Now, we can calculate the force of gravity:
F_g = (0.60 * 10^(-3) kg) * (9.8 m/s^2) = 5.88 * 10^(-3) N
Next, let's calculate the electrostatic force (F_e) acting on the ball. The formula for the electrostatic force is given by:
F_e = q * E * sin(theta)
where q is the charge on the ball, E is the electric field intensity, and theta is the angle between the thread and the vertical direction.
In this case, the electric field intensity (E) is given as 700 N/C, and the angle (theta) is 20 degrees.
Now we can solve for q:
F_e = F_g
q * E * sin(theta) = m * g
q = (m * g) / (E * sin(theta))
Plugging in the values:
q = ((0.60 * 10^(-3) kg) * (9.8 m/s^2)) / ((700 N/C) * sin(20 degrees))
q ≈ 3.17 * 10^(-6) C
The magnitude of the charge on the ball is approximately 3.17 * 10^(-6) C.
Given that the question asks for the magnitude and sign of the charge, we can see that the magnitude of the charge matches option (b) which is 0.0000032C. However, for the sign of the charge, it is positive because the electrostatic force is acting in the opposite direction (upwards) to the gravitational force. Therefore, the correct answer is 0.0000032C (option b).