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Note: 1 fC = 1 x 1015 C 2. In the figure a nonconducting rod of length L = 8.21 cm has charge -q = -4.33 fC uniformly distributed along its length. (a) What is the linear charge density of the rod? What are the (b) magnitude and (c) direction (positive angle relative to the positive direction of the x axis) of the electric field produced at point P, at distance a = 13.8 cm from the rod? What is the electric field magnitude produced at distance a = 50 m by (d) a particle of charge -q = -4.33 fC that replaces the rod?

Note: 1 fC = 1 x 1015 C 2. In the figure a nonconducting rod of length L = 8.21 cm has charge -q = -4.33 fC uniformly distributed along its length. (a) What is the linear charge density of the rod? What are the (b) magnitude and (c) direction (positive angle relative to the positive direction of the x axis) of the electric field produced at point P, at distance a = 13.8 cm from the rod? What is the electric field magnitude produced at distance a = 50 m by (d) a particle of charge -q = -4.33 fC that replaces the rod?

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Please help with part (b) (c) (d) Thanks
### Educational Content on Electric Fields and Linear Charge Distribution **Note:** 1 fC (femtocoulomb) = 1 x 10^(-15) coulombs #### Problem Statement: 2. In the figure provided, a nonconducting rod of length **L = 8.21 cm** has a charge **-q = -4.33 fC** uniformly distributed along its length. **Questions:** - **(a)** What is the linear charge density of the rod? - **(b)** What are the magnitude and - **(c)** Direction (positive angle relative to the positive direction of the x-axis) of the electric field produced at point **P**, at a distance **a = 13.8 cm** from the rod? - **(d)** What is the electric field magnitude produced at distance **a = 50 m** by a particle of charge **-q = -4.33 fC** that replaces the rod? #### Diagram Explanation: The diagram below illustrates the setup: ![Diagram Description]() - The rod (orange rectangle) extends from the origin to length **L**. - **P** is a point located at a distance **a** from the end of the rod along the x-axis. - The charge **-q** is uniformly distributed along the length **L** of the rod. #### Solution Approach: **(a) Linear Charge Density** The linear charge density (λ) is defined as the charge per unit length: \[ \lambda = \frac{q}{L} \] **(b) Magnitude of Electric Field at Point P** To determine the electric field at point **P** due to a uniformly charged rod, we typically integrate the contributions of differential charge elements along the length of the rod. **(c) Direction of Electric Field** The direction of the electric field produced by a negatively charged rod will be toward the rod (along the negative x-axis if the calculation is made correctly). **(d) Electric Field due to a Point Charge at a Distance \(a = 50 m\)** If the rod is replaced by a point charge of \(-q\) at the origin, the electric field at a distance **a** is calculated using Coulomb's Law: \[ E = \frac{k_e \cdot |q|}{a^2} \] where: - \( E \) is the magnitude of
Transcribed Image Text:### Educational Content on Electric Fields and Linear Charge Distribution **Note:** 1 fC (femtocoulomb) = 1 x 10^(-15) coulombs #### Problem Statement: 2. In the figure provided, a nonconducting rod of length **L = 8.21 cm** has a charge **-q = -4.33 fC** uniformly distributed along its length. **Questions:** - **(a)** What is the linear charge density of the rod? - **(b)** What are the magnitude and - **(c)** Direction (positive angle relative to the positive direction of the x-axis) of the electric field produced at point **P**, at a distance **a = 13.8 cm** from the rod? - **(d)** What is the electric field magnitude produced at distance **a = 50 m** by a particle of charge **-q = -4.33 fC** that replaces the rod? #### Diagram Explanation: The diagram below illustrates the setup: ![Diagram Description]() - The rod (orange rectangle) extends from the origin to length **L**. - **P** is a point located at a distance **a** from the end of the rod along the x-axis. - The charge **-q** is uniformly distributed along the length **L** of the rod. #### Solution Approach: **(a) Linear Charge Density** The linear charge density (λ) is defined as the charge per unit length: \[ \lambda = \frac{q}{L} \] **(b) Magnitude of Electric Field at Point P** To determine the electric field at point **P** due to a uniformly charged rod, we typically integrate the contributions of differential charge elements along the length of the rod. **(c) Direction of Electric Field** The direction of the electric field produced by a negatively charged rod will be toward the rod (along the negative x-axis if the calculation is made correctly). **(d) Electric Field due to a Point Charge at a Distance \(a = 50 m\)** If the rod is replaced by a point charge of \(-q\) at the origin, the electric field at a distance **a** is calculated using Coulomb's Law: \[ E = \frac{k_e \cdot |q|}{a^2} \] where: - \( E \) is the magnitude of
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