A uniform volume charge density of 80 uC/m is present throughout the region 8 mm 10 mm, find D, at r = 20 mm.
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- Y P L 13 In the figure above a nonuniformly charged rod of length L = 4.5 m lies along the x-axis with one end at the origin. The linear charge density (charge per length) is given by A = (3.8 x 10-9) 1.5 (where A has units of C/m when a has units of meters). Point P is located at the origin (the less densely charged end of the rod). What is the total charge on the rod? (This is given by Q = = Jdq= √ Adz.) Lok Ada 22 where What is the magnitude of the electric field at point P? (This will be given by E = A is now a function of a instead of a constant.)Density, density, density. (a) A charge -361e is uniformly distributed along a circular arc of radius 5.40 cm, which subtends an angle of 41°. What is the linear charge density along the arc? (b) A charge -361e is uniformly distributed over one face of a circular disk of radius 3.50 cm. What is the surface charge density over that face? (c) A charge -361e is uniformly distributed over the surface of a sphere of radius 4.60 cm. What is the surface charge density over that surface? (d) A charge -361e is uniformly spread through the volume of a sphere of radius 3.30 cm. What is the volume charge density in that sphere?An infinitely long cylindrical conducting shell of outer radius r1 = 0.10 m and inner radius r2 = 0.08 m initially carries a surface charge density σ = -0.45 μC/m2. A thin wire, with linear charge density λ = 1.1 μC/m, is inserted along the shells' axis. The shell and the wire do not touch and there is no charge exchanged between them. Part (A) What is the new surface charge density, in microcoulombs per square meter, on the inner surface of the cylindrical shell? Part (B) What is the new surface charge density, in microcoulombs per square meter, on the outer surface of the cylindrical shell? Part (C) Enter an expression for the magnitude of the electric field outside the cylinder (r > 0.1 m), in terms of λ, σ, r1, r, and ε0.
- A helium nucleus (mass = 6.64×10−27kg, net charge = +2e)is fired directly toward a spherical conductor on a radially inward path. The conductor, which is fixed in place, has radiusR= 0.55 m and surface charge densityσ= +12 nC/m2. If the helium nucleus is initially very far away from the conductor, then what initial speed must it be given so that it just barely avoids touching the surface of the conductor before being repelled back to infinity? Make sure to draw a voltage vs. position curve for the spherical conductor as part of your representation.An insulating solid sphere of radius a has a uniform bulk density ρ and a total positive charge Q. Calculate the magnitude of the electric field at a point outside the sphere.An infinite sheet of charge, oriented perpendicular to the x-axis, passes through x = 3 μC/m2. 0. It has a surface charge density o1 = A thick, infinite conducting slab, also oriented perpendicular to the x-axis, occupies the region between a = 2.6 cm and b = 4.6 cm. The conducting slab has a net charge per unit area of 02 = 78 µC/m2. (Recall that the surface charge densities oa and oh on the slab surfaces at a and b, respectively, sum to equal the net charge per unit area: oa + ob = 02.) 1) What is Ex(P), the value of the x-component of the electric field at point P, located a distance 7.8 cm from the infinite sheet of charge? N/C Submit 2) What is Ey(P), the value of the y-component of the electric field at point P, located a distance 7.8 cm from the infinite sheet of charge? N/C Submit + 3) What is Ex(R), the value of the x-component of the electric field at point R, located a distance 1.3 cm from the infinite sheet of charge? N/C Submit 4) What is Ey(R), the value of the…
- A -198.7 mC charge is placed at the center of a hollow conducting sphere. Find the Charge density (in C/m²) on the outside of the sphere if its radius is 6.47 cm and if it Contains zero net charge.Charge is distributed over a triangular region in the xy-plane bounded by the y-axis and the lines y = 5 – x and y = 1+ x. The charge density at a point (x, y) is given by o(x, y) = x + y, measured in coulombs per square meter (C/m 2). Find the total charge. Select one: а. 4 С Ов. 68 3 44 C 3 O c. O d. 20 37 C 3 е.A solid block of copper, which is a good conductor, has a cavity in its interior. Within the cavity, insulated from the conductor, is a point charge of +3.00 nC. The block of copper itself has an excess charge of -8.00 nC. How much charge is on (a) the outer surface of the block and (b) the surface of the cavity?
- Two isolated metallic solid spheres of radii R and 2R are charged such that both of these have same charge density σ. The spheres are located far away from each other, and connected by a thin conducting wire. Find the new charge density on the bigger sphere.Electric charge is distributed over the disk a2 + y < 20 so that the charge density at (x,y) is o(x, y) = 5 + x² + y² coulombs per square meter. Find the total charge on the disk.On a plastic disc of radius R = 10 cm, an electric charge per unit area has been distributed proportional to the distance to the center, the proportionality constant being c = 2 μC/m. Determine the total load of the disk: