The figure below shows four small charged spheres arranged at the corners of a square with side d = 25.0 cm. (Let q₁ = +4.00 nC, 92= +6.00 nC, 93 +9.00 nC, and 94 = +5.00 nC. Assume 93 is located at the origin and +x axis is to the right and the +y axis is up along the page. Express your answers in vector form.) 91 d 92 93 d 94 (a) What is the electric field at the location of the sphere with charge +9.00 nC? E = N/C (b) What is the total electric force exerted on the sphere with charge +9.00 nC by the other three spheres? 7 = N d
The figure below shows four small charged spheres arranged at the corners of a square with side d = 25.0 cm. (Let q₁ = +4.00 nC, 92= +6.00 nC, 93 +9.00 nC, and 94 = +5.00 nC. Assume 93 is located at the origin and +x axis is to the right and the +y axis is up along the page. Express your answers in vector form.) 91 d 92 93 d 94 (a) What is the electric field at the location of the sphere with charge +9.00 nC? E = N/C (b) What is the total electric force exerted on the sphere with charge +9.00 nC by the other three spheres? 7 = N d
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- \( q_1 = +4.00 \, \text{nC} \)
- \( q_2 = +6.00 \, \text{nC} \)
- \( q_3 = +9.00 \, \text{nC} \) (located at the origin)
- \( q_4 = +5.00 \, \text{nC} \)
The square's orientation is such that the \( +x \) axis extends to the right and the \( +y \) axis extends upward.
### Problem Statements
**(a) Calculate the electric field at the location of the sphere with charge \( +9.00 \, \text{nC} \)**
Express your answer in vector form:
\[ \vec{E} = \, \boxed{\text{N/C}} \]
**(b) Determine the total electric force exerted on the sphere with charge \( +9.00 \, \text{nC} \) by the other three spheres**
Express your answer in vector form:
\[ \vec{F} = \, \boxed{\text{N}} \]
### Conceptual Explanation
In this exercise, the goal is to find the electric field and force acting on a specific charge \( q_3 \) due to the presence of three other charges arranged in a square configuration. The electric field \( \vec{E} \) at a point in space due to a point charge is calculated using Coulomb's law:
\[ \vec{E} = k_e \frac{q}{r^2} \hat{r} \]
where:
- \( k_e \) is Coulomb’s constant \( \left( 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \right) \)
- \( q \) is the charge
- \( r \) is the distance between the charges
- \( \hat{r} \) is the unit vector in the direction of the force
The net electric field at the location of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a5ac3c6-e4ab-423a-91e1-ff33bdae0d07%2Fd9cfe1ea-77a5-4c5a-826b-272314ae3041%2Fq67c3jc_processed.png&w=3840&q=75)
Transcribed Image Text:## Electric Field and Electric Force in a Square Configuration
The figure below illustrates four small charged spheres positioned at the corners of a square with side length \( d = 25.0 \, \text{cm} \).
### Diagram
- \( q_1 = +4.00 \, \text{nC} \)
- \( q_2 = +6.00 \, \text{nC} \)
- \( q_3 = +9.00 \, \text{nC} \) (located at the origin)
- \( q_4 = +5.00 \, \text{nC} \)
The square's orientation is such that the \( +x \) axis extends to the right and the \( +y \) axis extends upward.
### Problem Statements
**(a) Calculate the electric field at the location of the sphere with charge \( +9.00 \, \text{nC} \)**
Express your answer in vector form:
\[ \vec{E} = \, \boxed{\text{N/C}} \]
**(b) Determine the total electric force exerted on the sphere with charge \( +9.00 \, \text{nC} \) by the other three spheres**
Express your answer in vector form:
\[ \vec{F} = \, \boxed{\text{N}} \]
### Conceptual Explanation
In this exercise, the goal is to find the electric field and force acting on a specific charge \( q_3 \) due to the presence of three other charges arranged in a square configuration. The electric field \( \vec{E} \) at a point in space due to a point charge is calculated using Coulomb's law:
\[ \vec{E} = k_e \frac{q}{r^2} \hat{r} \]
where:
- \( k_e \) is Coulomb’s constant \( \left( 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \right) \)
- \( q \) is the charge
- \( r \) is the distance between the charges
- \( \hat{r} \) is the unit vector in the direction of the force
The net electric field at the location of
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