A small plastic ball of mass m = 1.50 g is suspended by a string of length L = 21.5 cm in a uniform electric field, as shown in the figure below. If the ball is in equilibrium when the string makes a 0 = 19.0° angle with the vertical as indicated, what is the net charge on the ball? μC 10 E=1.00 x 10³ N/C L m
A small plastic ball of mass m = 1.50 g is suspended by a string of length L = 21.5 cm in a uniform electric field, as shown in the figure below. If the ball is in equilibrium when the string makes a 0 = 19.0° angle with the vertical as indicated, what is the net charge on the ball? μC 10 E=1.00 x 10³ N/C L m
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![**Problem Statement:**
A small plastic ball of mass \( m = 1.50 \, \text{g} \) is suspended by a string of length \( L = 21.5 \, \text{cm} \) in a uniform electric field, as shown in the figure below. If the ball is in equilibrium when the string makes a \( \theta = 19.0^\circ \) angle with the vertical as indicated, what is the net charge on the ball?
**Diagram Explanation:**
The diagram illustrates a small ball suspended by a string at an angle \(\theta\) from the vertical. The diagram is labeled with the following details:
- The ball is hung such that the string makes a \(19.0^\circ\) angle with the vertical.
- The length of the string is \(21.5 \, \text{cm}\).
- The uniform electric field (\(E = 1.00 \times 10^3 \, \text{N/C}\)) is depicted by orange arrows pointing toward the right.
- The coordinate system is shown with \(y\) as vertical and \(x\) as horizontal.
- The ball is marked with mass \(m\).
The question mark symbol indicates the location where the net charge on the ball is to be calculated.
**Solution Approach:**
To find the net charge on the ball, consider the forces acting on the ball in equilibrium:
1. Gravitational Force (\(F_g = mg\)), acting downward.
2. Tension in the string, which has vertical (\(T\cos\theta\)) and horizontal (\(T\sin\theta\)) components.
3. Electric Force (\(F_e = qE\)), acting horizontally due to the electric field.
Using equilibrium conditions:
- Sum of forces in the vertical direction equals zero:
\[
T\cos\theta = mg
\]
- Sum of forces in the horizontal direction equals zero:
\[
T\sin\theta = qE
\]
From these, solve for the net charge \( q \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c067e04-819e-445d-9345-defba0ea4f93%2F71bc9d80-9457-447b-b4df-139d136ec861%2Fzfc8yhf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A small plastic ball of mass \( m = 1.50 \, \text{g} \) is suspended by a string of length \( L = 21.5 \, \text{cm} \) in a uniform electric field, as shown in the figure below. If the ball is in equilibrium when the string makes a \( \theta = 19.0^\circ \) angle with the vertical as indicated, what is the net charge on the ball?
**Diagram Explanation:**
The diagram illustrates a small ball suspended by a string at an angle \(\theta\) from the vertical. The diagram is labeled with the following details:
- The ball is hung such that the string makes a \(19.0^\circ\) angle with the vertical.
- The length of the string is \(21.5 \, \text{cm}\).
- The uniform electric field (\(E = 1.00 \times 10^3 \, \text{N/C}\)) is depicted by orange arrows pointing toward the right.
- The coordinate system is shown with \(y\) as vertical and \(x\) as horizontal.
- The ball is marked with mass \(m\).
The question mark symbol indicates the location where the net charge on the ball is to be calculated.
**Solution Approach:**
To find the net charge on the ball, consider the forces acting on the ball in equilibrium:
1. Gravitational Force (\(F_g = mg\)), acting downward.
2. Tension in the string, which has vertical (\(T\cos\theta\)) and horizontal (\(T\sin\theta\)) components.
3. Electric Force (\(F_e = qE\)), acting horizontally due to the electric field.
Using equilibrium conditions:
- Sum of forces in the vertical direction equals zero:
\[
T\cos\theta = mg
\]
- Sum of forces in the horizontal direction equals zero:
\[
T\sin\theta = qE
\]
From these, solve for the net charge \( q \).
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