**Problem Statement:**An uncharged, nonconducting, hollow sphere of radius 30.0 cm surrounds a 10.0-µC charge located at the origin of a Cartesian coordinate system. A drill with a radius of 3.00 mm is aligned along the z axis, and a hole is drilled in the sphere. Calculate the electric flux through the hole.**Detailed Explanation:**- **Given Information:** - Hollow sphere characteristics: - Material: Nonconducting - Charge: Uncharged - Radius: 30.0 cm - Charge inside the sphere: - Magnitude: 10.0 µC - Location: Origin of Cartesian coordinate system - Drill characteristics: - Alignment: Along the z axis - Radius of drill: 3.00 mm - **Objective:** - Calculate the electric flux through the hole created by drilling the sphere along the z axis.**Concepts Involved:**1. **Electric Flux:** - Electric flux (Φ) through a surface is given by the integral of the electric field (E) over the area (A) of the surface: \[ \Phi = \int E \cdot dA \] - For a uniformly charged situation, the flux can be simplified using Gauss's Law.2. **Gauss's Law:** - States that the total electric flux through a closed surface is equal to the charge enclosed (Q_enc) divided by the permittivity of the medium (ε₀): \[ \Phi = \frac{Q_{\text{enc}}}{\epsilon_0} \] - For this problem, since the hole is very small in comparison to the sphere, we can assume the flux through the hole is a fraction of the total flux through the sphere's surface.**Calculation Insight:**- **Using Gauss's Law:** - The electric flux through the entire surface of the sphere can be calculated first. - For a sphere surrounding the charge, the flux through the spherical surface would be: \[ \Phi_{\text{total}} = \frac{Q_{\text{enc}}}{\epsilon_0} \] - Given Q_enc = 10.0 µC (which is 10.0 x 10⁻⁶ C) and

Answered: Image /qna-images/answer/dcc7a39c-d8d2-47cf-98d4-3cc6e28f8430.jpg

An uncharged, nonconducting, hollow sphere of radius 30.0 cm surrounds a 10.0-uC charge located at the origin of a Cartesian coordinate system. A drill with a radius of 3.00 mm is aligned along the z axis, and a hole is drilled in the sphere. Calculate the electric flux through the hole.

An uncharged, nonconducting, hollow sphere of radius 30.0 cm surrounds a 10.0-uC charge located at the origin of a Cartesian coordinate system. A drill with a radius of 3.00 mm is aligned along the z axis, and a hole is drilled in the sphere. Calculate the electric flux through the hole.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: R X

Q: The 6R³r The charge density of an insulating sphere of radius R is given as p(r)= Q = insulation…

A: I have written formula for total charge on insulating sphere

Q: Problem 12: A long straight wire has a uniform charge density of 227 µC per meter. A long…

Q: 6R³r The charge density of an insulating sphere of radius R is given as p(r) = The insulation sphere…

Q: (a) Two conducting spherical shells are concentric and isolated. The first spherical shell has…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: A solid conducting sphere of radius 2.00 cm has a charge of 7.80 µC. A conducting spherical shell of…

A: Introduction: Given: The radius of the solid conducting sphere is 2.00 cm. The charge on the solid…

Q: A solid non-conducting sphere has a non-uniform charge distribution of p = ar, where r is the radial…

Q: A 27 nC charge generates an electric field within an isolated chamber. At a point a distance d…

A: We know, the electric field is given by E=kqd2

Q: Two uniform spherical charge distributions (see figure below) each have a total charge of 94.8 mC…

A: Given The charge on both the sphere is q = 94.8 mC = 94.8 x 10-3 C. The distance between the…

Q: 5. A long cylinder of radius R₁ is surrounded by a concentric cylindrical tube with inner radius R₂…

Q: A ring of radius R=61 cm carries a charge of Q=+610 nC uniformly distributed over it. A point…

A: Radius of the ring, charge on the ring,…

Q: A very long uniform line of charge has charge per unit length 4.56 μC/m and lies along the x-axis. A…

A: According to the given data λ1=4.56 μC/m lies along x-axis λ2=-2.56 μC/m at y1=0.412 m line we need…

Q: p=a r, where a= 6.81 C/m* and r is in neters. What is the surface charge density inside the hollow…

Q: A charge of uniform linear density 1.90 nC/m is distributed along a long, thin, nonconducting rod.…

Q: A-140.1 mC charge is placed at the center of a hollow conducting sphere. Find the charge density (in…

Q: n infinitely long cylindrical conducting shell of outer radius r1 = 0.10 m and inner radius r2 =…

A: The outer radius is The inner radius is The surface charge density is The linear charge density is…

Q: Four solid plastic cylinders all have a radius 2.59 cm and length 6.54 cm. Find the charge of each…

A: Given data: Radius of the cylinder, r=2.55 cm = 0.0255 m Length of the cylinder, L=6.54 cm = 0.0654…

Q: A charge of uniform linear density 3.41 nC/m is distributed along a long, thin, nonconducting rod.…

A: Given thatLinear charge density To determine thatWhat is the surface charge density on the inner…

Q: A spherical conducting shell has an inner radius, b, and an outer radius, a. A point charge, 2q, is…

Q: Two uniform spherical charge distributions (see figure below) each have a total charge of 31.8 mC…

Q: ▼ Part C What is the strength of the electric field at point 8 cm from the center? Express your…

A: We know electric field inside a conductor is zero : So at 8 cm from center, E = 0 N/C

Q: There is a long cylinder that is made of nonconducting material. It has a cross section radius of…

Q: An infinite sheet charge of has a charge density of +60.51 pC/m2 and covers the entire x-y plane. A…

Q: A -198.7 mC charge is placed at the center of a hollow conducting sphere. Find the Charge density…

A: Given Charge at the center of the sphere is q=-198.7 mC=-198.7×10-3 C Radius of the sphere is r=6.47…

Q: A-140.1 mC charge is placed at the center of a hollow conducting sphere. Find the charge density (in…

Q: A circular metal plate of radius 17.2 cm carries a total charge of 1.01 μC and the charge is…

Q: A positively charged particle is held at the center of a spherical shell. The figure gives the…

A: Intersting problem from electrostatic (electrodynamics). Let's solve this problem by using Guass…

Q: An infinite sheet charge of has a charge density of +44.81 pC/m2 and covers the entire x-y plane. A…

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

100%

**Problem Statement:**

An uncharged, nonconducting, hollow sphere of radius 30.0 cm surrounds a 10.0-µC charge located at the origin of a Cartesian coordinate system. A drill with a radius of 3.00 mm is aligned along the z axis, and a hole is drilled in the sphere. Calculate the electric flux through the hole.

**Detailed Explanation:**

- **Given Information:**
- Hollow sphere characteristics:
- Material: Nonconducting
- Charge: Uncharged
- Radius: 30.0 cm
- Charge inside the sphere:
- Magnitude: 10.0 µC
- Location: Origin of Cartesian coordinate system
- Drill characteristics:
- Alignment: Along the z axis
- Radius of drill: 3.00 mm

- **Objective:**
- Calculate the electric flux through the hole created by drilling the sphere along the z axis.

**Concepts Involved:**

1. **Electric Flux:**
- Electric flux (Φ) through a surface is given by the integral of the electric field (E) over the area (A) of the surface:
\[
\Phi = \int E \cdot dA
\]
- For a uniformly charged situation, the flux can be simplified using Gauss's Law.

2. **Gauss's Law:**
- States that the total electric flux through a closed surface is equal to the charge enclosed (Q_enc) divided by the permittivity of the medium (ε₀):
\[
\Phi = \frac{Q_{\text{enc}}}{\epsilon_0}
\]
- For this problem, since the hole is very small in comparison to the sphere, we can assume the flux through the hole is a fraction of the total flux through the sphere's surface.

**Calculation Insight:**

- **Using Gauss's Law:**
- The electric flux through the entire surface of the sphere can be calculated first.
- For a sphere surrounding the charge, the flux through the spherical surface would be:
\[
\Phi_{\text{total}} = \frac{Q_{\text{enc}}}{\epsilon_0}
\]
- Given Q_enc = 10.0 µC (which is 10.0 x 10⁻⁶ C) and

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 2 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 -1.11 nC point charge is located inside a cavity of a hollow sphere of conducting material with charge 6.72 nC and of radius 10.0 cm. Calculate the electric field 0.473 m from the point charge in units of N/C. Assume answers are in the radial direciton such that if the field points radially away your answer will be positive and if the field points radially in your answer will be negative. Give your numerical result to 3 significant figures and type in the units after your numerical answer.
Please please type the answer instead of writing, thanks
An uncharged nonconductive hollow sphere of radius 15.0 cm surrounds a 13.0 μC charge located at the origin of a cartesian coordinate system. A drill with a radius of 1.00 mm is aligned along the z axis, and a hole is drilled in the sphere. Calculate the electric flux through the hole. N-m²/C Need Help? Submit Answer Read It
A conducting spherical shell of inner radius a = 3 cm and outer radius b = 8 cm is charged by a total charge Q = 4.8T µc. A point charge q = 1.6T µc is placed at the center of the spherical shell.The surface charge density at the outer surface (in 10-3 c/m?) is:
In the figure a thin glass rod forms a semicircle of radius r = 4.74 cm. Charge is uniformly distributed along the rod, with +q = 4.39 pC in the upper half and -q = -4.39 pC in the lower half. What is the magnitude of the electric field at P, the center of the semicircle? P. Number i Units
The figure shows a solid non-conducting sphere of radius a = 4.4 cm. It is surrounded by a charged conducting spherical shell of inner radius b = 15.3 cm and outer radius c = 24.8 cm. The inner sphere has a net charge of q1 = 9 nC and the conducting spherical shell has a net charge of q2 = -7 nC. a. What is the surface charge density on the inside surface of the spherical shell? b. What is the surface charge density on the outside surface of the spherical shell? c. What is the value of the electric field at a distance r = 58 cm from the centre of the spheres? Please use a negative value to indicate the electric field points toward the centre of the spheres and a positive value to indicate away from the centre of the spheres.
A charge of uniform linear density 2.00 nC/m is distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius = 4.20 cm, outer radius = 9.80 cm). The net charge on the shell is zero. (a) What is the magnitude of the electric field at distance r = 14.0 cm from the axis of the shell? What is the surface charge density on the (b) inner and (c) outer surface of the shell?
An infinitely long rod lies along the x-axis and carries a uniform linear charge density λ = 5 μC/m. A hollow cone segment of height H = 27 cm lies concentric with the x-axis. The end around the origin has a radius R1 = 8 cm and the far end has a radius R2 = 16 cm. Refer to the figure. a. Consider the conic surface to be sliced vertically into an infinite number of rings, each of radius r and infinitesimal thickness dx. Enter an expression for the electric flux differential through one of these infinitesimal rings in terms of λ, x, and the Coulomb constant k. b. Integrate the electric flux over the length of the cone to find an expression for the total flux through the curved part of the cone (not including the top and bottom) in terms of λ, H, and the Coulomb constant k. Enter the expression you find. c. Calculate the electric flux, in N•m2/C, through the circular end of the cone at x = 0. d. Calculate the electric flux, in N•m2/C, through the circular end of the cone at x = H. e.…
A charge Q = -10 nC sits at the center of a thick uncharged conducting spherical shell with inner radius R1 = 3.0 m and outer radius R2 = 4.0 m. Find the magnitude and direction of the electric field at a distance of (a) 2.0 m, (b) 3.5 m, and (c) 4.5 m away from the charge. R. R, 1.
A thin, copper washer of inner radius R = 54.0 mm and width d = 27.0 mm carries a unformly distributed total charge Q-9.00 nC. Determine the z-component of the electric field, Ez, due to the washer at a distance z = 12.0 cm along the washer's symmetry axis. Ez = -7.99 ×104 Incorrect N/C y Z