1- (6 points) A ring of radius R has a linear charge density of 1 =...
Consider a charged ring with radius R and uniform line charge density +λ.(a) Find the electric field at the center O of the ring. (b) What is the electric field at a field point P which is on the central axis with a distance z above the center? (c) Show that in the limit when z » R, the electric field reduces to the form Does this result physically make sense? Explain. (d) Using binomial approximation, , find the electric field at points along the...
In the figure, a ring 1.59 m in radius carries a linear charge density of 10nC/m uniformly distributed over it. A point charge Q = 100nC is placed at the center of the ring. Find the electric field strength at a point P, a distance of 5 from the ring. 1 OP
16a: An "are" of radius R and linear charge density λ-Xo sin φ lies in the xy plane. It extends an angle of o above and below the x-axis. Determine the electric field at the origin. b: Determine the z-component of the electric field at the point (0,0, zo) but this time assume that λ--X- IR
PROBLEM 2: A thick, spherical, insulating shell has an inner radius a and an outer radius b. The region a< r < b has a volume charge density given by p = A/r where A is a positive constant. At the center of the shell is a point charge of electric charge +q Determine the value of A such that the electric field magnitude, in the region a < r < b, is constant.
5. (**) Field of a uniform ring of charge The ring of radius R shown at right lies in the yz-plane and carries a uniformly distributed charge Q. (a) Find the electric field due to the ring of charge at any point on the X-axis. (b) Find the value of x for which the electric field is a maximum, and determine this maximum field strength. (c) On the axes below, sketch the magnitude of Ex versus x for points on...
2. A thin ring of radius R in the x - y plane is centered at the coordinate origin, and is charged with linear charge density λ which depends* on the polar angle θ as (9) λο sin(0), where 0 > 0, and θ . (a) Plot λ(0) for θ [0.2n]. (b) Before doing any calculations, sketch the electric field vector vector at the coor- - 0 is on the positive r-axis dinate origin in the direction you expect it...
a positive charge Q is evenly distributed in a ring of radius r, determine the potential and the electric field at a point x on the axis of the ring
Question A1 (12 marks] A sphere with radius R carries a charge density that is proportional to the square of the distance from the origin, i.e. p = kr2 for some constant k. (a) [3 marks] Calculate k if the total charge on the sphere is Q. (Hint: dt = r2 sin(O) dr do do ) (b) [3 marks) Write down Gauss's law in integral form. In which situations can it be used to directly calculate the electric field of...
Find the electric field due to a circular ring with charge density A and radius R Find the field here
An infinitely long straight wire is uniformly charged with a
positive linear charge density +?. It is surrounded by an
insulating hollow cylinder (also infinitely long) of inner radius R
and outer radius 2R. The hollow cylinder has a uniform charge
density ?.
(a) Determine the value of ? if the electric field vanishes at
every point outside the cylinder (r > 2R).
(b) Determine the electric field in the region 0 < r <
R.
(c) Determine the electric...