A rod of length L lies along the x axis with its left end at the origin. B It has a non-uniform charge density 1 = ax, where a is a positive constant. (a) Calculate the electric potential at point A. The point A is on the x axis in the negative side at a distance of d from the origin. (b) Calculate the electric potential at point B, which lies on the perpendicular bisector of the rod a distance b above the x axis. A

A rod of length L lies along the x axis with its left end at the origin. B It has a non-uniform charge density 1 = ax, where a is a positive constant. (a) Calculate the electric potential at point A. The point A is on the x axis in the negative side at a distance of d from the origin. (b) Calculate the electric potential at point B, which lies on the perpendicular bisector of the rod a distance b above the x axis. A

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter24: Electric Potential

Section: Chapter Questions

Problem 25P: A rod of length L (Fig. P24.25) lies along the x axis with its left end at the origin. It has a...

See similar textbooks

Related questions

Q: A rod of length L = 4.00 m with uniform charge of 6.90 nC/m is oriented along the y axis as shown in…

A: To calculate the electric potential at a point due to a line charge. Given:Length of rod: L=4.00…

Q: Problem 6: A ring of radius R = 7 cm lies in the y-z plane and is centered at the origin. The ring…

Q: An electron is at the origin. (a) Calculate the electric potential VA at point A, x = 0.410 cm. V…

A: Given data: a). From the given value, x=0.410 cm=0.410×10-2 m. b).Given value, x=0.420 cm=0.420×10-2…

Q: A solid aluminum sphere with radius a has an explicitly negative charge,−q. Concentric with the…

A: Given: The charge on the solid aluminum sphere is -q The charge on the Copper shell: +Q We know that…

Q: A graph of the x component of the electric field as a function of x in a region of space is shown in…

Q: A thin plastic rod of length d = 0.65 m lies along the x-axis with its midpoint at the origin. The…

A: Electric potential due to a charge at a point is given by- V=14πε0qr Charge per unit length is given…

Q: Positive charge Q is distributed uniformly along the x axis from x = -a/2 to x = +a/2. Point P is on…

A: Let Q denotes the positive charge distributed over the length a, r denotes the distance of point P…

Q: A graph of the x component of the electric field as a function of x in a region of space is shown in…

Q: olid aluminum sphere with radius a has an explicitly negative charge,−q. Concentric with the…

A: Given Data:Aluminum sphere with radius and charge It is concentric with a copper shell with an…

Q: A plastic rod has been bent into a circle of radius R= 6.00 cm. It has a charge Q=+100.0 pC…

Q: E, (N/C) A graph of the x component of the electric field as a function of x in a region of space is…

Q: A plastic rod has been bent into a circle of radius R = 6.00 cm. It has a charge Q=+100.0 pC…

A: Let Q1 and Q2 denotes the charge on the plastic, dQ denotes a small charge segment, R denotes the…

Q: bent into a circle of radius R-11.0 cm. It has a charge Q1+3.43 pC uniformly distributed along…

A: Electric potential = kqr . V= k (∫02πr/4Q12πrdr x 1r + ∫02πr.3/4Q22πrdr x 1r) We may solve this…

Q: A conducting spherical shell of inner radius b and outer radius c is concentric with a small metal…

A: The net charge enclosed in the system is Qnet=Q+(-Q)Qnet==0 According to the Gauss law, the…

Q: A rod of length L is lying on x-axis with left end at the origin and has a non-uniformly linear…

Q: A plastic rod has been bent into a circle of radius R = 5.03 cm. It has a charge Q, = +7.42 pC…

Q: A spherical conductor whose center is at point O and radius R = 20 cm, is given a charge Q = + 100…

A: Answer:- Given Charge (Q) = + 100 uC = 100 × 10-6 C = 10-4 C Radius (R) = 20 cm = 0.2 m Coulomb…

Q: A positive charge is evenly distributed on the surface of a metal sphere centered at the origin of…

Q: A plastic rod has been bent into a circle of radius R= 6.00 cm. It has a charge Q=+100.0 pC…

Q: A graph of the x component of the electric field as a function of x in a region of space is shown in…

A: On a vertical axis, the electric field is given byThe y and z components of the electric field are…

Q: A uniform line of charge with charge/length λ and length 2l lies along the x-axis extending from x=…

A: The linear charge density of the line of charge is λ, the length of the line of charge is 2l…

Q: A rod of length L = 4.00 m with uniform charge of 9.50 nC/m is oriented along the y axis as shown in…

Q: A thin insulating rod is bent into a semicircular arc of radiu a total electric charge Q is…

A: A thin insulating rod is bent into a sernicrcular arc of radius a.

Q: An infinitely long metal cylinder has radius R0 and charge per unit length λ. It is held at…

Q: A charge Q= +5.60 µC is uniformly distributed on a thin cylindrical plastic shell. The radius, R, of…

A: Charge (Q) = 5.60 μC =5.60×10-6 C Radius of the shell (R) = 4.50 cm =4.50×10-2 cm. Assumption:…

Q: A ring of radius R = 4cm lies in the y-z plane and is centered at the origin. The ring carries a…

A: The objective of the question is to derive an equation for the electric field along the positive…

Q: A non-conducting rod (see diagram below) has a uniform charge density magnitude 1 = 3.00 x 10-6 C/m.…

Q: The linear non-uniform charge distribution given by lamda = bx, where b is a constant, lies along…

Q: A solid aluminum sphere with radius a has an explicitly negative charge,−q. Concentric with the…

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 rod of length L lies along the x axis with its left end at the origin.
B
It has a non-uniform charge density 1 = ax, where a is a positive
constant.
(a) Calculate the electric potential at point A. The point A is on the
x axis in the negative side at a distance of d from the origin.
(b) Calculate the electric potential at point B, which lies on the
perpendicular bisector of the rod a distance b above the x axis.
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

Given

VIEW

Electric potential at point A -1

VIEW

Electric potential at point A -2

VIEW

Electric potential at point B - 1

VIEW

Electric potential at point B - 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 5 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?
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.
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
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 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?
Figure P26.44 shows a rod of length = 1.00 m aligned with the y axis and oriented so that its lower end is at the origin. The charge density on the rod is given by = a + by, with a = 2.00 C/m2 and b = 1.00 C /m2. What is the electric potential at point P with coordinates (0, 25.0 cm)? A table of integrals will aid you in solving this problem.
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)?
The three charged particles in Figure P20.11 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. Figure P20.11
Figure P26.80 shows a wire with uniform charge per unit length = 2.25 nC/m comprised of two straight sections of length d = 75.0 cm and a semicircle with radius r = 25.0 cm. What is the electric potential at point P, the center of the semicircular portion of the wire? FIGURE P26.80
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.
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?
Three particles with equal positive charges q are at the corners of an equilateral triangle of side a as shown in Figure P20.10. (a) At what point, if any, in the plane of the particles is the electric potential zero? (b) What is the electric potential at the position of one of the particles due to the other two particles in the triangle? Figure P20.10