Show that for a charged circular ring of radius a and total charge Q, the electric field anywhere inside the plane of the ring would be zero if the electric field was inversely proportional to r not r2. Your answer is partly verbal and graphical.
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Show that for a charged circular ring of radius a and total charge Q, the electric field anywhere inside the plane of the ring would be zero if the electric field was inversely proportional to r not r2. Your answer is partly verbal and graphical.
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- An infinite sheet charge of has a charge density of +60.51 pC/m2 and covers the entire x-y plane. A second infinite sheet of charge has a charge density of −78.1 pC/m2 covers the entire y-z plane. What is the magnitude of the electric field at any point not on either surface?What is the percent difference between the electric field produced by the finite disk and by an infinite sheet with the same charge per unit area at x = 0.40 cm?Consider two infinite planes of charge, both parallel to the x-y plane. The first plane is located at z = 0 m, and has a charge density of +6.4 x 10-12 C/m2. The second plane is located at z = 5 m, and has a charge density of +4 x 10-12 C/m2. Calculate the magnitude of electric field at z = 36 m. Use ε 0 = 8.9 x 10-12 F/m. (Please answer to the fourth decimal place - i.e 14.3225)
- Consider a ring of charge. The ring is in the x-y plane and has a radius of 3.5 m. The charge per angle as a function of angle α (in radians) around the ring is given by dQ/dα = 6.9 α (nC/rad). Calculate the z-component of the electric field, in N/C, at the coordinate (0, 0, 9 m). Use k = 9 x 109 N m2 / C2. (Please answer to the fourth decimal place - i.e 14.3225)Point P sets above an infinite line of charge 2 m in the positive z direction. The line of charge itself has a charge density ? of -5.0 x 10⁶ C/m. What is the magnitude of the electric field at point P?A solid non-conducting sphere of radius R carries a uniform charge density. At a radial distance r 1 = 6R the electric field has a magnitude E 0. What is the magnitude of the electric field at a radial distance r 2 = R/6 as a multiple of E 0 ?
- 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.A positively charged line with linear charge density λ is pictured along the x-axis with length L. Starting with the differential form of Coulomb’s Law () derive an equation for the electric field at point P at (x=a, y=0) k, a, L, and λ.Assume you have a line of positive charge with a linear charge density of 10.0 µC/m. Assume that this line of charge is infinitely long and lies on the z-axis (which is perpendicular to both the x- and y-axes). a) Find the strength and direction of the electric field associated with this line of charge at (0.5 m, 0 m, 0 m) The strength of the field at the stated point is N/C and the direction of the field at the stated point is O-x O+x O-y O+y O-z O+z b) Find the strength and direction of the electric field associated with this line of charge at (0 m, 0.5 m, 5 m) The strength of the field at the stated point is N/C and the direction of the field at the stated point is O-x O+x O-y O+y O-z O+z c) Find the strength and direction of the electric field associated with this line of charge at (2.0 m, 0 m, Om) The strength of the field at the stated point is N/C and the direction of the field at the stated point is O-x O+x O-y O+y O-z O+z
- There is a +5C charge at the center of a hollow sphere made of a perfect conductor. The hollow sphere has a net charge of +2C, an inner radius of 0.5 m and an outer radius of 0.75 m. Calculate the electric field as a function of distance from the +5C charge and the charge on each surface of the hollow sphere.Consider a line of charge with a uniform charge density of 35.0 nC/m. It is placed along the line y = − 15.0 cm between the points x = 0 and x = 40.0 cm. Find the electric field vector (both direction and magnitude) due to this line charge distribution at the origin.A charge distribution creates the following electric field throughout all space: E(r, 0, q) = (3/r) (r hat) + 2 sin cos sin 0(theta hat) + sin cos p (phi hat). Given this electric field, calculate the charge density at location (r, 0, p) = (ab.c).