Answered: A disk of radius R has a nonuniform…

A disk of radius R has a nonuniform surface charge density sigma = Cr, where C is a constant and r is measured from the center of the disk. Find (by direct integration) the potential at P.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter26: Electric Potential

Section: Chapter Questions

Problem 45PQ: The charge density on a disk of radius R = 12.0 cm is given by = ar, with a = 1.40 C/m3 and r...

See similar textbooks

Related questions

Q: Given the potential function V = x2y(z+3), determine the electric potential at (3, 4, -6)

A: Given data V=x2yz+3x2y

Q: Two concentric rings, of radii R and 2R, lie on the y-z plane and at the origin as shown in the…

Q: Problem 3.18 The potential at the surface of a sphere (radius R) is given by Vo = k cos 30, where k…

A: Find the potential inside and the outside of the circle by possion's equation and gauss law.

Q: Consider an infinite line charge with linear charge density 1. At a distance r from the line, the…

Q: What are (a) the charge and (b) the charge density on the surface of a conducting sphere of radius…

Q: The scalar electric potential in empty space is given as Vx'y(z+3) (v). Find E and Pv

Q: thin, spherical, conducting shell of radius R is mounted on an isolating support and charged to a…

A: The electric potential energy here is, The initial potential energy equals the initial kinetic…

Q: Find the electrical potential V for a linear charge of length l and charge density pl at a point b…

Q: The circular arc shown, with radius R and spanning an angle of 30°, has a total charge Q uniformly…

Q: For a spherical surface with radius 0.1m and is charged by 2*10-8C, the electric potential V at r =…

A: Given: The radius of spherical surface R = 10 cm. = 0.1 m. Charge on spherical surface q = 2×10-8 C

Q: The electric potential in a region of space is V(r) = Axz/y, with A a constant. What is the electric…

Q: A glass ring of radius 5.0 cm is painted with a charged paint such that the charge density around…

Q: Consider a potential field in cylindrical coordinates and a point P in the same coordinate system.…

Q: A hollow spherical shell carries a volume charge density in the region a b (b) For the case where b…

A: Since you have asked multiple subparts only the first three subparts are solved for you. If you want…

Q: A finite linear charge distribution has a total charge Q and length l. The linear charge density is…

Q: Consider the electric potential $(z, y, 2) = Vo a(1/m) - ry(V/m2)+ ay:(V/m) It is given that the…

Q: A long cylindrical shell of 6 cm radius has a uniformly distributed charge with a density of 8.5 µC…

A: Given : R=0.06m r=0.04m ρ=8.5×10-9C/m The electric potential difference…

Q: Find the potential relative to the surface at a point that is distance r from the axis, assuming r >…

Q: Three charges , and are placed respectively at the corners A, B, and C of an equilateral triangle…

Q: What is the electric potential 2.5 x 10-15 m away from a proton (+e)?

Q: On a sphere surface of radius R, the surface charge density is defined by the function o= ACose (A…

A: SOlution: Given that σ=Acosθ to find the potential inside and outside

Q: k (1 – cos 0) The potential is specified on the surface of a hallow sphere of radius R. Find the…

Q: Find the electric potential inside and outside a uniformly charged spherical shell of radius R

A: we determine electric potential inside and outside by using simple intigrating electric field…

Q: Find the potential at the origin when there is a uniform line charge of 5 nanocoulomb formed by the…

Q: If a charged spherical conductor of radius 10 cm has potential v at a point distant 5 cm from its…

Q: On a square wireframe with side length a in empty space, there is a linear charge density ρl. Write…

A: Recall V=kQ/r Here we have considered x,y and z axes as shown and points A and B's coordinates have…

Q: Using Gauss’s Law and the relation between electric potential and electric field, show that the…

A: According to the Gauss law:The electric flux through any closed surface is=Qε0electric…

Q: What is the excess charge on a conducting sphere of radiusr=0.35 m if the potential of the sphere is…

A: Conductors have an important property which states that no electric field can penetrate inside the…

Q: Suppose one of the point charges (+2e) got loose from the honeycomb setup in problem #1 and got…

Q: a non-conducting hollow sphere has outer radius R and inner radius R/2 and carries a uniform volume…

A: Given: A non-conducting hollow sphere has an outer radius R and inner radius R/2 and carries a…

Q: Find the electric potential difference between two charged spherical surfaces with charge +q and –q,…

A: Given quantities: charge on first surface = + q radius of first spherical surface = Ra charge on…

Q: Derive this equation for Potential of A uniform line of charge, using integration with limits as 0…

A: Small element dz is taken in the long rod and then we will integrate to get potential of whole rod…

Q: A solid spherical conductor of radius R= 0.3 m has a net charge Q= 6 nC. What is the electric…

Q: The electric potential of a spherically symmetric charge distributic -) = R[5 – 4(4)°, V (r) =; ]…

Q: Find the electric potential distribution of charged spherical surface with the charge q and the…

A: Electric potential at a point in the field is defined as the work done in moving a unit positive…

Q: For a spherical surface with radius 0.1m and is charged by 4*10-8C, the electric potential V at r =…

A: Given values: Radius, R=0.1 m Charge, q=4×10-8 C Distance, r=20 cm 14πε0=9×109 Nm2/C2

Q: The radius and surface charge density of a uniformly charged spherical shell are 20 cm and, 0.3…

A: we have to find the electric potential at 40 cm away from the centre and 15 cm away from the centre.…

Q: Consider a spherical shell of radius Rand a charge +Q, uniformly distributed over the surface. A…

A: Given , a point on the surface of spherical shell P Radius of shell = R Charge on shell = +Q…

Q: (а) Find expressions for the total electric potential at the origin (z = 0), at the center of the…

A: Solution: a) charge at the center is = q Potential at center due to this charge element is given…

Q: Two infinitely large plates at a distance of L from each other are uniformly charged with surface…

Q: What is the electric potential 8.1m from a point charge of 7.7C, assuming that the potential os 0 at…

A: At any point around a point charge, the electric potential is given by, Here, K, q and r represent…

Q: A cylindrical shell of radius R, and height his charged with charge that is uniformly distributed…

A: (a) is correct

Q: A point charge Q is concentric with two spherical shells with radii a and b, and charges −2Q and…

Q: A large sheet of paper lying in the x-y plane carries a uniform surface charge o. A narrow annulus…

A: Given:- A large sheet of paper lying in the x-y plane carries a uniform surface charge density σ A…

Q: Given the potential function V = x2y(z+3), determine the electric potential at (3, 4, -6

A: Given data

Q: Compute for the absolute potential for every of the following distances from a charge of 2 μC: when…

Concept explainers

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

A disk of radius R has a nonuniform surface charge density sigma = Cr, where C is a constant and r is measured from the center of the disk. Find (by direct integration) the potential at P.

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

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

A filament running along the x axis from the origin to x = 80.0 cm carries electric charge with uniform density. At the point P with coordinates (x = 80.0 cm, y = 80.0 cm), this filament creates electric potential 100 V. Now we add another filament along the y axis, running from the origin to y = 80.0 cm, carrying the same amount of charge with the same uniform density. At the same point P, is the electric potential created by the pair of filaments (a) greater than 200 V, (b) 200 V, (c) 100 V, (d) between 0 and 200 V, or (e) 0?
A metallic sphere of radius 2.0 cm is charged with +5.0C charge, which spreads on the surface of the sphere uniformly. The metallic sphere stands on an insulated stand and is surrounded by a larger metallic spherical shell, of inner radius 5.0 cm and outer radius 6.0 cm. Now, a charge of 5.0C is placed on the inside of the spherical shell, which spreads out uniformly on the inside surface of the shell. If potential is zero at infinity, what is the potential of (a) the spherical shell, (b) the sphere, (c) the space between the two, (d) inside the sphere, and (e) outside the shell?
The charge density on a disk of radius R = 12.0 cm is given by = ar, with a = 1.40 C/m3 and r measured radially outward from the origin (Fig. P26.45). What is the electric potential at point A, a distance of 40.0 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.
The electric potential inside a charged spherical conductor of radius R is given by V = keQ/R, and the potential outside is given by V = keQ/R, Using Er = dV/dr, derive the electric field (a) inside and (b) outside this charge distribution.
An electric potential exists in a region of space such that V = 8x4 2y2 + 9z3 and V is in units of volts, when x, y, and z are in meters. a. Find an expression for the electric field as a function of position. b. What is the electric field at (2.0 m, 4.5 m, 2.0 m)?
Two large charged plates of charge density 30C/m2 face each other at a separation of 5.0 mm. (a) Find the electric potential everywhere, (b) An electron is released from rest at the negative plate; with what speed will it strike the positive plate?
(a) Find x L limit of the potential of a finite uniformly charged rod and show that it coincides with that of a point charge formula, (b) Why would you expect this result?
How many electrons should be removed from an initially uncharged spherical conductor of radius 0.300 m to produce a potential of 7.50 kV at the surface?
A small spherical pith ball of radius 0.50 cm is painted with a silver paint and then -10 C of charge is placed on it. The charged pith ball is put at the center of a gold spherical shell of inner radius 2.0 cm and outer radius 2.2 cm. (a) Find the electric potential of the gold shell with respect to zero potential at infinity, (b) How much charge should you put on the gold shell if you want to make its potential 100 V?
The three charged particles in Figure P25.22 are at the vertices of an isosceles triangle (where d = 2.00 cm). Taking q = 7.00 C, calculate the electric potential at point A, the midpoint of the base.
For the arrangement described in Problem 26, calculate the electric potential at point B, which lies on the perpendicular bisector of the rod a distance b above the x axis. Figure P20.26
An electron moving parallel to the x axis has an initial speed of 3.70 106 m/s at the origin. Its speed is reduced to 1.40 105 m/s at the point x = 2.00 cm. (a) Calculate the electric potential difference between the origin and that point. (b) Which point is at the higher potential?