Question

(5%) Problem 7: A solid disk of radius R = 17 cm lies in the y-z plane with the center at the origin. The disk carries a uniformly distributed total charge Q = 35 µC. A point P is located on the positive half of the x-axis a distance 25 cm from the origin. Refer to the diagram, where the y- and z-axes lie in the plane of the screen and the x-axis points out of the screen. 25% Part (a) Enter an expression for the surface charge density ? in terms of the total charge and radius of the disk. ?= 25% Part (b) Consider a thin ring of the disk of width dr located a distance r from the center. Enter an equation for the infinitesimal charge in this thin ring in terms of Q, R, r, and dr. 25% Part (c) Calculate the electric potential at P, in kilovolts. 25% Part (d) Calculate the magnitude of the electric field at the point P in units of meganewtons per coulomb.

          (5%) Problem 7: A solid disk of radius R = 17 cm lies in the y-z plane with the center at the
origin. The disk carries a uniformly distributed total charge Q = 35 µC. A point P is located on the
positive half of the x-axis a distance 25 cm from the origin. Refer to the diagram, where the y- and
z-axes lie in the plane of the screen and the x-axis points out of the screen.
25% Part (a) Enter an expression for the surface charge density ? in terms of the total charge and radius of the disk.
?=
25% Part (b) Consider a thin ring of the disk of width dr located a distance r from the center. Enter an equation for the infinitesimal charge in this thin
ring in terms of Q, R, r, and dr.
25% Part (c) Calculate the electric potential at P, in kilovolts.
25% Part (d) Calculate the magnitude of the electric field at the point P in units of meganewtons per coulomb.

Show more…

(5%) Problem 7: A solid disk of radius R = 17 cm lies in the y-z plane with the center at the
origin. The disk carries a uniformly distributed total charge Q = 35 µC. A point P is located on the
positive half of the x-axis a distance 25 cm from the origin. Refer to the diagram, where the y- and
z-axes lie in the plane of the screen and the x-axis points out of the screen.
25% Part (a) Enter an expression for the surface charge density ? in terms of the total charge and radius of the disk.
?=
25% Part (b) Consider a thin ring of the disk of width dr located a distance r from the center. Enter an equation for the infinitesimal charge in this thin
ring in terms of Q, R, r, and dr.
25% Part (c) Calculate the electric potential at P, in kilovolts.
25% Part (d) Calculate the magnitude of the electric field at the point P in units of meganewtons per coulomb.

Added by Dennis P.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

05/21/2024

Step 1

**Part (a): Expression for the surface charge density** Show more…

Show all steps

lock

Thanks for your feedback!

Problem 7: A solid disk of radius R = 17 cm lies in the y-z plane with the center at the origin. The disk carries a uniformly distributed total charge Q = 35 µC. A point P is located on the positive half of the x-axis a distance 25 cm from the origin. Refer to the diagram, where the y- and z-axes lie in the plane of the screen and the x-axis points out of the screen. Part (a) Enter an expression for the surface charge density σ in terms of the total charge and radius of the disk. Part (b) Consider a thin ring of the disk of width dr located a distance r from the center. Enter an equation for the infinitesimal charge in this thin ring in terms of Q, R, r, and dr. Part (c) Calculate the electric potential at P, in kilovolts. Part (d) Calculate the magnitude of the electric field at the point P in units of meganewtons per coulomb.

Play audio

Feedback

Powered by NumerAI

Adi S and 96 other subject Physics 101 Mechanics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:02 Given that, given radius r is equal to 20 cm and total charge q is equal to 40 mc.

00:14 And area of this a is equal to pi r square.

00:19 Surface charge density according to the equation.

00:22 Surface charge density rho s is equal to q upon pi r square.

00:39 Consider our ring of charge at a radical distance r.

00:43 The charge contained in width dr so dq is equal to q is equal to rho s into 2 pi r e to dr is equal to 2 pi into rho s and r dr.

01:05 The potential at p is due to ray.

01:08 A is equal to aq upon 4 pi epsilon naught is equal to 2 pi rho s rdr upon 4 pi epsilon naught r square plus pi square 1 by 2.

01:33 Where a is equal to a is equal to r square plus x square whole power 1 upon 2.

01:42 So the potential due to entire disc v is equal to limit 0 to r dv is equal to rho s upon 2 epsilon naught and integration limit 0 to a r dr upon r square plus x square value of a to whole power 1 upon 2.

02:07 So, v is equal to rho s upon 2 epsilon naught into r square plus x square whole power 1 upon 2 and limit 0 to r.

02:21 So, v is equal to rho s upon 2 epsilon naught r square plus x square whole power 1 upon 2 limit 0 to r.

02:30 So, v is equal to rho s upon 2 epsilon naught into r square plus x square to whole power 1 upon 2 minus x.

02:40 And this is equation first.

02:42 After rho at s is equal to q upon phi r square is equal to 40 upon 3 .14 substituting values into 0 .2 whole square...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later