= 1. A point charge, Q₁ = 10µC, is located at P₁(1, 2, 3) in free space, while Q₂ -5μC is at P₂(1,2, 10). Find the vector force exerted on Q₂ by Q₁.
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- A particle with charge q on the negative x axis and a second particle with charge 2q on the positive x axis are each a distance d from the origin. Where should a third particle with charge 3q be placed so that the magnitude of the electric field at the origin is zero?What is the field strength of the electric vector E at the origin as a result of all three charges and what is its direction(in polar coordinates)Eight 25-nC point charges in free space are located symmetrically on a circle of radius0.2 m centered at the origin in the z = 0 plane. (a) At what point on the z axis is |E| amaximum? (b) What is |E| max?
- Eight identical point charges of Q(Coulomb) each are located at the corners of a cube of side length a, with one charge at the origin, and with the three nearest charges at (a, 0, 0), (0, a, 0), and (0, 0, a). Find an expression for the total vector force on the charge at P(a/2, a/2, a/2), assuming free space.In Figure 1, an insulating rod is bent into a semicircle of radius R. A charge -Q is uniformly distributed along its top half (for 0 < theta < pi/2) while a charge +Q is uniformly distributed along its bottom half (for -pi/2<theta< 0). Find the lectrostatic force in unit vector notation, acting on an electron with charge -e which is located at the origin O.The Long line is carrying a uniform charge density of λ=7.9μC/m is 10.0cm above a large surface with uniform charge density σ=2.3mC/m2. What perpendicular distances s (in cm) from the line charge would an α particle (moving parallel to the line) feel no force?
- A particle charges with three points of ?1 = 3.2 × 10 C, ?2 = 2.5 × 10 C and ?3 = 4.6 × 10C, are located in free space of Mars at points with Cartesian coordinates (2, 3, 1), (−3, 2, −1) and (1, 2, 3), respectively. Calculate:(a) The electric field, ? at (3.5, 2.4, 1.0)(b) The force on a 6 × 10C charge located at (3.0, 2.8, 1.5)A point charge, Q1 = -4.2 μC, is located at the origin. A rod of length L = 0.35 m is located along the x-axis with the near side a distance d = 0.45 m from the origin. A charge Q2 = 10.4 μC is uniformly spread over the length of the rod. Part (a) Consider a thin slice of the rod, of thickness dx, located a distance x away from the origin. What is the direction of the force on the charge located at the origin due to the charge on this thin slice of the rod? Part (b) Write an expression for the magnitude of the force on the point charge, |dF|, due to the thin slice of the rod. Give your answer in terms of the variables Q1, Q2, L, x, dx, and the Coulomb constant, k. Part (c) Integrate the force from each slice over the length of the rod, and write an expression for the magnitude of the electric force on the charge at the origin. Part (d) Calculate the magnitude of the force |F|, in newtons, that the rod exerts on the point charge at the origin.A +7.00 µC particle is located at x = 0.0 cm, and a –9.0 μC particle is located at x = 40.0 cm. Where must a positive test charge be placed along the x–axis so that the net electric force on it is zero? Hint: In a FBD, place the test charge left of x = 0 cm, in between the two source charges, and right of x = 40 cm. Sketch the direction and relative magnitude of the net force at each location and determine where it might be possible for the net force to be zero. Then set the magnitudes of the forces equal to each other.
- A very small sphere with positive charge q=+ 5.00 μC is released from rest at a point 1.70 cm from a very long line of uniform linear charge density λ=+ 2.00 μC/m . What is the kinetic energy of the sphere when it is 3.90 cm from the line of charge if the only force on it is the force exerted by the line of charge? Express your answer with the appropriate units. K = ?The charges and coordinates of two charged particles held fixed in an xy plane are q1 = 2.01 μC, x1 = 4.64 cm, y1 = 0.418 cm and q2 = -4.91 μC, x2 = -1.77 cm, y2 = 1.82 cm. Find the (a) magnitude and (b) direction (with respect to +x-axis in the range (-180°;180°]) of the electrostatic force on particle 2 due to particle 1. At what (c) x and (d) y coordinates should a third particle of charge q3 = 3.70 μC be placed such that the net electrostatic force on particle 2 due to particles 1 and 3 is zero?Determine E at (2, 0, 2)m due to three standard charge distributions as follows: a uniform sheet at x = 0 m with ρs1=(13π)nCm2ρs1=(13π)nCm2, a uniform sheet at x = 4 m with ρs2=(−13π)nCm2,ρs2=(−13π)nCm2, and a uniform line at x = 6 m, y = 0 m with ρl=−2nCmρl=−2nCm.