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[15 Points] The figure shows a rod with its central axis along the y-axis and a ring with its central axis along the x-axis. • The rod, located at a distance y = 13 [cm] from the origin, has a length L = 9 [cm] and a charge Qrod = 57 [pc] uniformly distributed. • The ring, located at a distance d = 24 [cm] from the origin, has a radius R = 4 [cm] and a charge Qring = 85 [PC] uniformly distributed. 0 y [cm] R x [cm]
1. [2 Points] Calculate the magnitude of the electric field created by the rod at the origin. Erod = [N/C] 2. [2 Points] What is the direction of the electric field vector created by the rod at the origin. 3. [2 Points] Calculate the magnitude of the electric field created by the ring at the origin. Ering = 4. [2 Points] What is the direction of the electric field vector created by the ring at the origin. 5. [2 Points] Calculate the linear charge density of the rod and select the corresponding unit. λrod [N/C] = (
6. [2 Points] Calculate the linear charge density of the ring. λring 7. [3 Points] The rod is moved upward so that the magnitude of the electric field of the rod is now 10.4 [N/C]. Find the new distance y between the origin and the rod. y = [cm]
[25 points] The expression of the electric potential is given to be: V(x, y, z) = 5x² + 12xz+y 1. [5 points] What is the x-component of the electric field vector (Ex)? O-1 O-10x - 12z 010x + 12z O-12x 2. [5 points] What is the y-component of the electric field vector (Ey)? O-1 01 O-12x O-10x - 12z
3. [5 points] What is the z-component of the electric field vector (E₂)? O-10x - 12z 012x O-12x 0-1 4. [5 points] Suppose that Ē = (-3x²) Î + ( 4y²) + (-2z²) k, what is the electric field at point P of coordinates (-3; -3; 0) [m]? Î+ k Ē [V/m] = + 4. [5 points] Suppose that Ē = (-3x²)i + ( 4y²) Ĵ + (-2z²) k, what is the electric potential difference along the x-axis between -1 [m] and 2 [m]? AV = [V]