Consider an annulus of inner radius a and outer radius b and surface charge density +σ as shown in figure 6. The electric potential of the annulus at a point on the z-axis is given by: V(z) = σ/2ε0 [ sqrt(b2+z2) - sqrt(a2+z2) ] a) Find an expression for the electric field E of the annulus. b) Sketch the direction of the electric field calculated in part a.

Consider an annulus of inner radius a and outer radius b and surface charge density +σ as shown in figure 6. The electric potential of the annulus at a point on the z-axis is given by: V(z) = σ/2ε0 [ sqrt(b2+z2) - sqrt(a2+z2) ] a) Find an expression for the electric field E of the annulus. b) Sketch the direction of the electric field calculated in part a.

Related questions

Q: The charge density on a disk of radius R = 12.2 cm is given by aar, with a = 1.48 µC/m³ and r…

A: Given data R = 0.122 m a = 1.48×10-6 cm3y = 36 ×1100 = 0.36 mε° = 8.85 ×× 10-12c2Nm2

Q: Activity 1: Electric Potential 1. Two charges Q1=+5nC and Q2=-7nC are separated by 8 cm. Qi e +5 nC…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: An infinitely long insulating cylinder has radius a and volume charge density ρ. This cylinder is…

A: given in question that outer surface of conducting shell is at zero potential. and from the property…

Q: There are two conduction spheres shown in the figure above, the larger sphere has a radius of R and…

Q: potential energy of the spherical system!

A: Given Data : Charge density p(r) = p0r2 (in spherical polar Coordinates) To Find : potential…

Q: A ring of radius R = 9 cm lies in the y-z plane and is centered at the origin. The ring carries a…

A: Given: R = 9 cm Q = 61 μC

Q: A uniform electric field of magnitude 340 V/m is directed in the negative y direction as shown in…

A: Given E=340 V/m Along negative y-axis A=(-0.650 , -0.200) B=(0.350,0.200) Required VB-VA

Q: Determine the electric potential due to a uniformly charged ring (total charge Q = 6.0 nC and radius…

A: Electrostatic.

Q: Derive an expression for the magnitude of the electric field on the axis of the ring i.e. Z, using…

Q: A circular disk of radius a has uniform charge density of p across its surface. The normal of the…

Q: The charge density on a disk of radius R = 11.8 cm is given by o = ar, with a = 1.36 µC/m³ and r…

Q: A force F of magnitude 920 lb is applied to point C of the bar AB as shown. Determine both the x-y…

A: A force F of magnitude 920 lb is applied to point C of the bar AB as shown in the figure. We need to…

Q: The charge density on a disk of radius R = 12.6 cm is given by d = ar, with a = 1.34 µC/m³ and r…

Q: A ball of conductor with radius RA = 2 cm is charged + 2Q. The ball located centrally to the hollow…

Q: The electric potential on the axis of a uniform ring of charge density A (shown in Figure 3) is…

Q: Knowledge of the electric field at a given point in space is insufficient to fully determine the…

Q: Given a sphere of radius R made of a dielectric material that is isotropic and linear with a…

A: Given, Radius = R Electric Field = E0

Q: The charge density on a disk of radius R= 13.0 cm is given by car, with a = 1.44 μC/m³ and r…

Q: The potential in a region of space due to a charge distribution is given by the expression V = ax2z…

A: The solution of the problem is given below

Question

Consider an annulus of inner radius a and outer radius b and surface charge density +σ as shown in figure 6. The electric potential of the annulus at a point on the z-axis is given by:

V(z) = σ/2ε0 [ sqrt(b²+z²) - sqrt(a²+z²) ]

a) Find an expression for the electric field E of the annulus.

b) Sketch the direction of the electric field calculated in part a.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A charged conducting spherical shell of radius R = 3 m with total charge q = 23 μC produces the electric field given by E⃗ (r)={014πϵ0qr2r̂ forforr<Rr>R(PICTURE ATTACHED OF EQUATION) a. Enter an expression for the electric potential inside the sphere ( r < R ) in terms of the given quantities, assuming the potential is zero at infinity. V(r)= b. Calculate the electric potential, in volts, at radius r inside the charged shell. V(r) =
The drawling shows a plot of the electric potential V versus the displacement s. Determine the electric field in the region from 0.2 to 0.6 m. Be sure to include the proper + or - sign.
5) The electric potential of a solid insulating sphere of radius R with electric charge Q is described by the equations; V (r) : KQ for r> R, V(R) KQ for r= R, r and, V (r) = KQ for r
A disk of radius R placed in the xy-plane carries a non-uniform charge density ? = ?? ?/?2where k is constant (you may use the integral below). Find: a. The units of k b. The total charge on the disk in terms of k and R c. The electric potential at point P, a distance y from its center d. The energy of a point charge (??) placed at P
mm. 2
The charge density on a disk of radius R = 11.2 cm is given by σ = ar, with a = 1.34 μC/m³ and r measured radially outward from the origin (see figure below). What is the electric potential at point A, a distance of 48.0 cm above the disk? Hint: You will need to integrate the nonuniform charge density to find the electric potential. You will find a table of integrals helpful for performing the integration. V R A
A uniformly charged insulating rod of length 12.0 cm is bent into the shape of a semicircle as shown in the figure below. The rod has a total charge of -9.00 μC. Find the electric potential at O, the center of the semicircle. x All the charge is equidistant from the center. Would the potential change if we gathered all of the charge into a single point at this same distance? MV Ⓡ
Over a certain region of space, the electric potential is V = 7x - 2x2y + 2yz2. Find the expression for the x component of the electric field over this region. (Use the following as necessary: x, y, and z.) Ex = Find the expression for the y component of the electric field over this region. Ey = Find the expression for the z component of the electric field over this region. Ez = What is the magnitude of the field at the point P, which has coordinates (7, 0, -7) m? N/C
A solid insulating sphere of radius a = 4 cm is fixed at the origin of a co-ordinate system as shown. The sphere is uniformly -118 µC/m³. Concentric with charged with a charge density p = the sphere is an uncharged spherical conducting shell of inner radius b = 12.8 cm, and outer radius c = 14.8 ст. P(40)
A thin rod extends along the x-axis from x = −a to x = a . The rod carries a positive charge +Q uniformly distributed along its length 2a with charge density λ, as shown in Figure attached. a) Use dV = 1/4πε0 ∫ dq/r to show that the electric potential at point P is given by: V(x) = (λ/4πε0) ln(x + a/x − a) b) What is the electric potential of the rod at x = 4a and x = 2a? c) What is the electric potential difference between x = 4a and x = 2a?
Problem 2: A hollow cylindrical shell of length L and radius R has charge Q uniformly distributed along its length. What is the electric potential at the center of the cylinder? a) Compute the surface charge density n of the shell from its total charge and geometrical parameters. Vcenter = 1 Q 2 In 4л€ L t₂ S² b) Which charge dq is enclosed in a thin ring of width dz located at a distance z from the center of the cylinder (shown in Fig.2)? Which potential dV does this ring create at the center (you need to use the formula derived in the textbook for the potential of a charged ring along its axis). dz c) Sum up the contributions from all the rings along the cylinder by integrating dV with respect to z. Show that (The integral that you need to use here is d dt √²+a² R² + 1/2 + 1/1/20 √√R² +4-4 L² R2 L R FIG. 2: The scheme for Problem 2 [2 = ln(t + √₁² + a²) 1².) 2
Q1. What is the electric potential of a dipole on the y-axis at large distances? 1 qd 1 qd (c) V = 2nɛ, r? 1 qd 4πε r (a) V = 0 (b) V = (d) V = 2πε, r y Q2. Find the monopole term in the multi-pole expansion of the electric potential on the z- axis for a flat circular charged disk of radius R and charge density o (r,q) = krʻ cosʻ q, where k is a constant and r, q are polar coordinates with the origin at the disk's centre.