A semicircle of radius a is in the first and Figure second quadrants, with the cen- ter of curvature at the origin. Positive charge +Q is distrib- uted uniformly around the left half of the semicircle, and nega- tive charge -Q is distributed uniformly around the right half of the semicircle (Fig. P21.86). What are the magnitude and direction of the net electric field a the origin produced by this distribution of charge? : +0

infinitely long cylinder has a cylindrical hole in the middle. The inner radius of the cylinder is R1 and the outer radius of the cylinder is R2. The volume charge density, p, is distributed evenly throughout the volume. Find the magnitude of the electric field at distance r from the central axis for the cases when r R2. R

A cube has positive charge +Q in all corners except for one, which has a negative point charge - Q. Let the distance from any corner to the center of the cube be r. What is the magnitude and direction of the of electric field at the center of the cube (point P)?

32. Assume the magnitude of the electric field on each face of the cube of edge1.00 m in Figure P24.32 is uniform and the directions of the fields on each face are as indicated. Find (a) the net electric lux through the cube and ( the net charge inside the cube. (c) Could the net charge be a single point charge? ON/C 200 N/C 200 N/C 850N/C 200N/C 5.ON/C

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A conductor contains a hollow cavity in which there is a +100 nC point charge. A charged rod transfers -50 nC to the conductor. Afterwards, what is the charge a. On the inner wall of the cavity wall, b. On the exterior surface of the conductor?

+ a + A hollow sphere has a uniform volume charge density of 1.46 nC/m3. The inner radius is a = 11.7 cm and the outer radius is b = 46.8 cm. What is the magnitude of the electric field at 4.68 cm from the center of the sphere? What is the magnitude of the electric field at 145 cm from the center of the sphere?

d Circular 3. Space vehicles traveling through Earth's radiation belts can intercept a significant number of electrons. The resulting charge buildup can damage electronic components and disrupt operations. Suppose a spherical metal satellite 1.3 m in diameter accumulates 2.4 μC of charge in one orbital revolution. (a) Find the resulting surface charge density. (b) Calculate the magnitude of the electric field just outside the surface of the satellite, due to the surface charge.

A non-uniform thin rod is bent into an arc of radius R. The linear charge density λ of the rod depends on θ and is given byλ= λ0/cos θwhere λ0 is a positive constant. The arc extends from θ = π/2 to θ = 3π/2  Sketch the direction of the resultant electric field at the origin.Calculate the magnitude of the electric field E⃗ .