An infinite cylinder of radius R = 11.9 m, has a volume charge density of p(r) = 0.6r × 10-12 C/m³ Using Gauss's law, what is the electric field (in N/C) at a distance of r = 9 m from the cylinder's axis.
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- A charge distribution that is spherically symmetric but not uniform radially produces an electric field of magnitude E = Kr4, directed radially outward from the center of the sphere. Here r is the radial distance from that center, and K is a constant.What is the volume density r of the charge distribution?A quarter-disc in the first quadrant has a surface charge density given by K cos φ C/m2. If the radius of the discis b, calculate the electric field at a point P(0, 0, −hCharge is uniformly distributed around a ring of radius R = 2.40 cm, and the resulting electric field magnitude E is measured along the ring’s central axis (perpendicular to the plane of the ring). At what distance from the ring’s center is E maximum?
- What is the total flux passing through a 10 cm × 6 cm surface in a regionwhere the electric flux density is 2700 μC/m2?In a symmetrical electric field of 58.3 x 101 N/C , a flat circle with a diameter of 30 cm is positioned. When the circle's face is perpendicular to the field lines, what is the electric flux through it?Consider the electric field E=34i^−7j^+5k^. What is the electric flux through a cube with side length a?
- A uniform volume charge distribution ρv=5 (nC/m3) exists in a sphere that has a radius of a=3 cm. What is the magnitude of the electric field intensity at a distance R=4 cm? (Use Gauss’s Law)The nonuniform charge density of a solid insulating sphere of radius R is given by = cr2 (r R), where c is a positive constant and r is the radial distance from the center of the sphere. For a spherical shell of radius r and thickness dr, the volume element dV = 4r2dr. a. What is the magnitude of the electric field outside the sphere (r R)? b. What is the magnitude of the electric field inside the sphere (r R)?What is the magnitude of the electric field just above the middle of a large, flat, horizontal sheet carrying a charge density of 98.0 nC/m2?
- The figure below shows a non-conducting spherical shell with a charge density of ρ = + 2 x 10-6 C/m^3. If the inner and outer radii of the sphere a = 10 cm and b = 20 cm, respectively, find the electric field strength E as a function of the distance from the center of the sphere's shell r, with r from zero to 30 cm.An infinite, uniform, line of charge is on the x-axis. The linear charge density is (lambda), with units of C/m. Find an expression for the electric field at a particular y-value on the y-axis at x=0, using Gauss's Law. Do this problem as if (lambda) is positive -- the answer is valid regardless of the sign. If (lambda) = 2.5 nC/m, and y = 8 cm, calculate the electric field.A square 10 cm long is in a region where there exists a uniform 2.0 kN/C electric field normal to the surface of the square. Evaluate the electric flux?