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Two charges +1 μC and +13 μC are placed along the x axis, with the first charge at the origin (x = 0) and the second charge at x = +1 m. Find the magnitude and direction of the net force on a -8 nC charge when placed at the following locations below. Overall Hint a. halfway between the two charges: magnitude of force is direction is Select an answer b. on the axis at x = -0.5 m: magnitude of force is Magnitude of force is degrees below-axis mN, and the is Select an answer c. at the coordinate (x, y) = (1 m, 0.5 m) (half a meter above the +13 µC charge in a direction perpendicular to the line joining the two fixed charges): Hint for (c) mN, and the direction is mN, and the direction

Two charges +1 μC and +13 μC are placed along the x axis, with the first charge at the origin (x = 0) and the second charge at x = +1 m. Find the magnitude and direction of the net force on a -8 nC charge when placed at the following locations below. Overall Hint a. halfway between the two charges: magnitude of force is direction is Select an answer b. on the axis at x = -0.5 m: magnitude of force is Magnitude of force is degrees below-axis mN, and the is Select an answer c. at the coordinate (x, y) = (1 m, 0.5 m) (half a meter above the +13 µC charge in a direction perpendicular to the line joining the two fixed charges): Hint for (c) mN, and the direction is mN, and the direction

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### Electrostatic Force Calculation for Multiple Charges on an Axis In this exercise, we have two charges: - A charge of +1 μC is placed at the origin (x = 0). - A charge of +13 μC is placed at x = +1 m. We are tasked with determining the magnitude and direction of the net force on a -8 nC charge at various positions on the xy-plane. #### a) **Halfway Between the Two Charges:** - **Position:** Midpoint between 0 m and +1 m, which is x = 0.5 m. - **Required:** - Magnitude of force in mN - Direction of force (choose from provided options) #### b) **On the x-axis at \(x = -0.5\) m:** - **Position:** x = -0.5 m on the x-axis. - **Required:** - Magnitude of force in mN - Direction of force (choose from provided options) #### c) **At the Coordinate \((x, y) = (1 m, 0.5 m)\):** - Located half a meter above the +13 μC charge in a direction perpendicular to the line joining the two fixed charges. - **Hint for (c):** - The direction is given as degrees below the -x axis. - **Required:** - Magnitude of force in mN - Direction in degrees below the -x axis This problem involves the application of Coulomb’s law to calculate the forces due to each charge at the specified positions. Ensure you use vector addition to find the net force. --- For detailed calculations and steps, students are encouraged to revisit the principles of Coulomb’s law, vector addition, and trigonometry. Analyzing each position involves calculating the force exerted by each charge on the -8 nC charge and then combining these forces vectorially to determine both the magnitude and direction of the net force.
Transcribed Image Text:### Electrostatic Force Calculation for Multiple Charges on an Axis In this exercise, we have two charges: - A charge of +1 μC is placed at the origin (x = 0). - A charge of +13 μC is placed at x = +1 m. We are tasked with determining the magnitude and direction of the net force on a -8 nC charge at various positions on the xy-plane. #### a) **Halfway Between the Two Charges:** - **Position:** Midpoint between 0 m and +1 m, which is x = 0.5 m. - **Required:** - Magnitude of force in mN - Direction of force (choose from provided options) #### b) **On the x-axis at \(x = -0.5\) m:** - **Position:** x = -0.5 m on the x-axis. - **Required:** - Magnitude of force in mN - Direction of force (choose from provided options) #### c) **At the Coordinate \((x, y) = (1 m, 0.5 m)\):** - Located half a meter above the +13 μC charge in a direction perpendicular to the line joining the two fixed charges. - **Hint for (c):** - The direction is given as degrees below the -x axis. - **Required:** - Magnitude of force in mN - Direction in degrees below the -x axis This problem involves the application of Coulomb’s law to calculate the forces due to each charge at the specified positions. Ensure you use vector addition to find the net force. --- For detailed calculations and steps, students are encouraged to revisit the principles of Coulomb’s law, vector addition, and trigonometry. Analyzing each position involves calculating the force exerted by each charge on the -8 nC charge and then combining these forces vectorially to determine both the magnitude and direction of the net force.
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