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 central axis but with z « R.
(e) Suppose we now place a negative charge –q on a point on the central axis that is very close to O, but not exactly at O. What will happen to the charge -q after we release it from rest?
Consider a charged ring with radius R and uniform line charge density +λ.
The figure shows a ring of outer radius R = 23.0 cm, inner radius r = 0.160R, and uniform surface charge density σ = 8.00 pC/m2. With V = 0 at infinity, find the electric potential at point P on the central axis of the ring, at distance z = 2.10R from the center of the ring.
2. Charged ring A ring with an inner radius r. and outer radius & has a uniform surface charge density o. a) Find V (2), the electric potential along the central axis of the ring.. Set zoo at the ring center, and V (2 00) 50: b) Simplify the solution to part cas if z=r=R and ra= R/
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...
A uniform line charge that has a linear charge density λ = 4.1 nC/m is on the x axis between x = 0 to x-5.0 m (a) what is its total charge? (b) Find the electric field on the x axis at x = 6 m 1 23e 10 × N/C ci the electric field on the x axis at x 8.0 m N/C (d) Find the electric field on the x axis at x 300 m N/C (e)Estimate the...
All the charge in a ring of charge Q is the same distance r from a point P on the ring axis. a) Electric charge Q is distributed uniformly around a thin ring of radius a (Fig. 23.20). Find the potential at a point P on the ring axis at a distance x from the center of the ring. b) Find the electric field at P using the appropriate denotative relationships
6. Consider a line charge with uniform charge density λ lying on the x-axis from z =-L to 0. a) Determine the electric field a distance y above the right end of the line charge (point P in the figure) and a distance r to the right of the line charge (point P2 in the figure). P2 b) In lecture you saw the electric field of an infinite line charge. Now we will consider a "semi-infinite" line charge; that is,...
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
2. Figure shows a ring of radius R 4m and a point particle located at the center of the ring. Point P is on the central z axis, at distance z 3 m above the ring. The ring is charged with the uniform linear charge density of 1 10 C/m. What is the charge of the point particle, Q, if the net electrical field at point P is zero? -3 m R-4 m
A uniform circular ring of charge Q and radius r in the xy-plane is centered at the origin. (a) Derive a formula for the (z-directed) electric field E(z) at any point on the +z-axis, and graph this for-∞ < z < ∞ (indicate direction as ±; note E(-z) =-E(z). (b) At what value of z is E(z) maximal, and what is this maximum? (c) Sketch the field lines-note the bottleneck!