Four point charges a1, 42, 93, and q4 are positioned at points (11.0),(0,12),(-15,0), and (0,-8), respectively. a) write the net electric field due to these |- 4p C charges at the origin in vector form using the unit vectors î and j. 7x(cm) 5pC b) Calculate the magnitude and direction of the vector you found in part a.
Four point charges a1, 42, 93, and q4 are positioned at points (11.0),(0,12),(-15,0), and (0,-8), respectively. a) write the net electric field due to these |- 4p C charges at the origin in vector form using the unit vectors î and j. 7x(cm) 5pC b) Calculate the magnitude and direction of the vector you found in part a.
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![### Problem Set
**1)**
Four point charges \( q_1, q_2, q_3, \) and \( q_4 \) are positioned at points \((1,0)\), \((0,12)\), \((-1,5,0)\), and \((0,-8)\), respectively.
- **a)** Write the net electric field due to these charges at the origin in vector form using the unit vectors \( \hat{i} \) and \( \hat{j} \).
- **b)** Calculate the magnitude and direction of the vector you found in part (a).
- **c)** Write the net electric force on \( q_4 \) in vector form using \( \hat{i} \) and \( \hat{j} \).
- **d)** Calculate the magnitude and direction of the vector you found in part (c).
Make sure you use the correct units in your calculations and final answers. Coordinates are in \((x, y)\) form.
**Diagram Explanation:**
The diagram indicates four point charges placed on an xy-coordinate system. The specific charges and positions are as follows:
- \(6 \mu C\) is at (1,0)
- \(5 \mu C\) is at (0,12)
- \(3 \mu C\) is at (-1.5,0)
- \( -4 \mu C\) is at (0,-8)
---
**2)**
An electron’s position and velocity at \( t = 0 \) are given by the vectors:
\[ \vec{r_0} = 0.50 \, m \, \hat{j} \]
\[ \vec{v_0} = 4 \times 10^3 \, m/s \, \hat{i} - 4 \times 10^3 \, m/s \, \hat{j} \]
There exists a uniform electric field given by:
\[ \vec{E} = -100 \, N/C \, \hat{j} \]
Ignoring gravity, find:
- **a)** The acceleration vector \( \vec{a} \) of the electron.
- **b)** The position vector \( \vec{r} \) when \( \vec{v} = 4 \times 10^3 \, m/s \, \hat{i} \)
- **c](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F73881bad-35e9-478f-80dc-30ed83e5c525%2Fefa80d0f-9fec-434d-8736-87f0ee089874%2F4yw4kjl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Set
**1)**
Four point charges \( q_1, q_2, q_3, \) and \( q_4 \) are positioned at points \((1,0)\), \((0,12)\), \((-1,5,0)\), and \((0,-8)\), respectively.
- **a)** Write the net electric field due to these charges at the origin in vector form using the unit vectors \( \hat{i} \) and \( \hat{j} \).
- **b)** Calculate the magnitude and direction of the vector you found in part (a).
- **c)** Write the net electric force on \( q_4 \) in vector form using \( \hat{i} \) and \( \hat{j} \).
- **d)** Calculate the magnitude and direction of the vector you found in part (c).
Make sure you use the correct units in your calculations and final answers. Coordinates are in \((x, y)\) form.
**Diagram Explanation:**
The diagram indicates four point charges placed on an xy-coordinate system. The specific charges and positions are as follows:
- \(6 \mu C\) is at (1,0)
- \(5 \mu C\) is at (0,12)
- \(3 \mu C\) is at (-1.5,0)
- \( -4 \mu C\) is at (0,-8)
---
**2)**
An electron’s position and velocity at \( t = 0 \) are given by the vectors:
\[ \vec{r_0} = 0.50 \, m \, \hat{j} \]
\[ \vec{v_0} = 4 \times 10^3 \, m/s \, \hat{i} - 4 \times 10^3 \, m/s \, \hat{j} \]
There exists a uniform electric field given by:
\[ \vec{E} = -100 \, N/C \, \hat{j} \]
Ignoring gravity, find:
- **a)** The acceleration vector \( \vec{a} \) of the electron.
- **b)** The position vector \( \vec{r} \) when \( \vec{v} = 4 \times 10^3 \, m/s \, \hat{i} \)
- **c
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