Q1
10 Points
Three point charges with equal charge of Q = 1.8⋅10−10 C are placed at three vertices of an
equilateral triangle with side length a = 3 cm. What is the direction and magnitude of the
electric (Coulomb) force on each on charge Q in point 3? Sketch the Coulomb force vector on
the figure below. The coordinates on the figure below are in cm.
y
3
Q (0,2.6)
1
Q (-1.5,0)
2
(0,0)
Q (1.5,0)
x
Q2 10 points
Universe means for r from zero to positive infinity, and for all angle values for φ and θ.
Q3
10 points
Three infinite uniform sheets of charge are located in free space as follows:
3 nC/m2 at z = −4 m, 6 nC/m2 at z = 1 m, and −8 nC/m2 at z = 4 m. Find electric field intensity
vector E at the point P (0,0,3). Sketch the charged planes and the point P. Sketch the
streamlines of electric field. Use superposition principle and the expression of electric field
intensity for a charge plane to solve this problem. All dimensions are in meters.
Q4 Problem 3.2. from textbook with the sketch
10 Points
An electric field intensity vector in free space is E=(5z2/ε0) az [V/m]. Find the total
charge contained within a cube centered at the origin, of 4-m side length, in which
all sides are parallel to coordinate axes (and therefore each side intersects an axis
at +2 or -2). Sketch the coordinate system and the cube. Use Gauss law to solve this
problem.