The black surface shown in the figure is a section of a cone with apex P at the origin, a bottom base at z = -h and a top base at z = -0.5h. The cone's top and bottom circular cross sections have radii 0.5h and h, respectively. If the cone has a uniform positive surface charge density o, then the electric potential VP at the cone's apex P is: 0.5h 0.5h h O konhv2/2 -konh O konhv2/2 O konh
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- The thin plastic rod of length L = 18.2 cm in the figure has a nonuniform linear charge density λ= cx, where c= 24.8 pC/m. (a) With V=0 at infinity, find the electric potential at point P₂ on the y axis at y D=4.90 cm. (b) Find the electric field component Ey at P₂. (a) Number i (b) Number i D d- Units V Units V/mAn infinitely long metal cylinder has radius R0 and charge per unit length λ. It is held at potential V0, which you should use as the reference point for this problem. The cylinder is solid (not hollow) and in electrostatic equilibrium. (a) Find the electric potential outside the cylinder, for a distance r > R0 from the center of the cylinder. (b) Find the electric potential inside the cylinder, at a distance r < R0 from the center of the cylinder.For a sphere of radius R = 12.1 m that is charged with a non-uniform volume charge density: b p(r) = as =ar + with a = figure). 6.8 x 10-12 C/m² and b = 6.6 × 10-12 C/m² and r is the distance from the center of the sphere (see R Calculate the electric potential at distance r = 8.5 m from the center. Assume that the potential on the surface of the sphere equals to zero, that is (R) = 0. 21.0 x
- In the figure a plastic rod having a uniformly distributed charge Q = -20.5 pC has been bent into a circular arc of radius 1.94 cm and central angle 120°. With V = 0 at infinity, what is the electric potential in volts at P, the center of curvature of the rod? R Units V Number i 9.51A body is charged with a uniform charge density p = 3.1 nC/m³. A spherical cavity is created inside the body with radius R = 0.58 m (all the charges that were inside the sphere were taken out of the body). Before the cavity was created the electric potential at point O (at the center of the cavity) was 40 = 102 V. What is the potential at O after creating the cavity?The linear non-uniform charge distribution given by lamda = bx, where b is a constant, lies along the axis from x = 0 to x = 0.2 m. If b = 20 nC/m² and V = 0 at infinity, what is the electric potential at (a) the origin and (b) the point y = 0.15 m on the y-axis?
- A solid aluminum sphere with radius a has an explicitly negative charge,−q. Concentric with the aluminum sphere is a copper spherical shell with inner radius b, outer radius c, and an explicitly positive charge, +Q. Assume that the magnitude of the positive charge on the copper shell is greater than the magnitude of the negative charge on the aluminum sphere, and take the electric potential at infinity as zero. Enter an expression for the electric potential, V, that is valid for aA thin circular disc of radius a has a total charge Q uniformly distributed over it. It lies in the x - y plane, centered on the origin. The charge density on the disc is p(F) = e ng² 8(2') for x2 + y2 ≤a² and 0 elsewhere. Calculate (a) the electrostatic potential and (b) the electric field at a general point z on the positive z axis.