A uniform electric field given by E = (2.35i − 5.60j) ✕ 105 N/C
permeates a region of space in which a small negatively charged sphere of mass 1.65 g is suspended by a light cord (see figure below). The sphere is found to be in equilibrium when the string makes an angle
θ = 23.0°.
webassign.net/katzpse1/24-p-053.png
THe gravitational force is down, so figure the tension on the cord (mg/cos23). Now figure from that tension, figure vertical and horizontal components of that tension: Vertical force=tension*sin23; Horizontal= tension:*cos23
now you need to set those two forces equal to the electric force.
In the vertical: tension*sin23=5.6e5*q and
horizontal: tension:*cos23=2.35e5*q
That should allow you to solve for q. Check my thinking..
To find the charge of the small negatively charged sphere, we can use the principles of electrostatics and equilibrium.
First, let's consider the gravitational force acting on the sphere. It can be calculated using the formula:
F_gravity = m * g
Where:
F_gravity is the gravitational force,
m is the mass of the sphere,
g is the acceleration due to gravity (9.8 m/s^2).
Given:
Mass of the sphere (m) = 1.65 g = 1.65 * 10^(-3) kg
Acceleration due to gravity (g) = 9.8 m/s^2
Now, let's calculate the gravitational force acting on the sphere:
F_gravity = 1.65 * 10^(-3) kg * 9.8 m/s^2
F_gravity ≈ 1.617 * 10^(-5) N
Next, let's consider the electrostatic force acting on the sphere. The electrostatic force can be calculated using the formula:
F_electric = q * E
Where:
F_electric is the electrostatic force,
q is the charge of the sphere, and
E is the electric field.
Given:
Electric field (E) = (2.35i - 5.60j) * 10^5 N/C
Now, since the sphere is in equilibrium, the electrostatic force and the gravitational force must be equal in magnitude, but opposite in direction.
Therefore, we have:
|F_electric| = |F_gravity|
Solving for q:
q * E = m * g
q = (m * g) / E
Substituting the given values:
q = (1.65 * 10^(-3) kg * 9.8 m/s^2) / ((2.35i - 5.60j) * 10^5 N/C)
Now, to find the charge of the sphere, we need to evaluate this expression.