Consider a hemispherical (half of a sphere) surface that carries a uniform surface charge density Ps = 2 C/m². This hemisphere is centered at the origin and exists at r = a, n/2 < 0 < n and 0 < $ < 2n. In other word, this looks like a bowl that is open at the top. Show that the electric field at the centre (* = 0) of this hemisphere is Ē = (in units of v/m)? (The surface charge is only on the curved surface of this hemisphere. By symmetry, you should note that the E field is pointing in the positive Z direction. Assume the permittivity of free space, Eg , everywhere.)

Consider a hemispherical (half of a sphere) surface that carries a uniform surface charge density Ps = 2 C/m². This hemisphere is centered at the origin and exists at r = a, n/2 < 0 < n and 0 < $ < 2n. In other word, this looks like a bowl that is open at the top. Show that the electric field at the centre (* = 0) of this hemisphere is Ē = (in units of v/m)? (The surface charge is only on the curved surface of this hemisphere. By symmetry, you should note that the E field is pointing in the positive Z direction. Assume the permittivity of free space, Eg , everywhere.)