A point charge (m = 1.0 g) at the end of an insulating string of length L = 46 cm (Fig. 16-66) is observed to be in equilibrium in a uniform horizontal electric field of E = 8800 N/C, when the pendulum's position is as shown in Fig. 16-66, with the charge d = 1.0 cm above the lowest (vertical) position. If the field points to the right in Fig. 16-66, determine the magnitude and sign of the point charge.
What is Magnitude? C
The magnitude of the point charge is not given in the information provided. The information only includes the mass (1.0 g), the length of the string (46 cm), and the magnitude of the electric field (8800 N/C). The magnitude of the point charge cannot be determined without additional information.
To determine the magnitude of the point charge, we can use the concept of electric force and equilibrium.
1. Start by considering the forces acting on the point charge. In this scenario, the only force acting on the charge is the force due to the electric field.
F = E * Q, where F is the force, E is the electric field strength, and Q is the charge.
2. Since the charge is in equilibrium, the force due to the electric field should be equal to the weight of the charge.
F = m * g, where m is the mass of the charge, and g is the acceleration due to gravity.
3. Expressing the force due to the electric field as F = E * Q and the weight as F = m * g, we can set them equal to each other and solve for the charge.
E * Q = m * g
4. Rearrange the equation to isolate the charge (Q).
Q = (m * g) / E
5. Plug in the given values: m = 1.0 g (convert to kg), g = 9.8 m/s^2, and E = 8800 N/C.
Q = (0.001 kg * 9.8 m/s^2) / 8800 N/C
6. Calculate the magnitude of the charge.
Q = 1.11 × 10^-7 C
Therefore, the magnitude of the point charge is approximately 1.11 × 10^-7 C.
Without the figure, I am not certain.
The horizontal force is Eq. The vertical force is mg. It moves some angle theta from the vertical.
TanTheta=Eq/mg
SinTheta=1/46
so figure theta from that, then figure q from knowing theta.