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Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

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Electricity and Magnetism

Electric Flux

Concept Quizzes

Field Lines and Field Strength
Electric Flux
Gauss' Law
Conductors
Problem Solving

Challenge Quizzes

Level 2-3

Problem solving - Flux and Gauss' law

Consider an infinitely long, very thin metal tube with radius \(R=2.90\text{ cm}.\) The above figure shows a section of it. If the linear charge density of the cylinder is \(\lambda=1.50 \times 10^{-8} \text{ C/m},\) what is the approximate magnitude of the electric field at radial distance \(r=2R?\)

The value of the permittivity constant is \(\varepsilon_0=8.85 \times 10^{-12} \text{ C}^2\text{/N}\cdot\text{m}^2.\)

\[4.65\times10^{3}\text{ N/C} \] \[ 3.49 \times 10^{3} \text{ N/C} \] \[ 1.16 \times 10^{3} \text{ N/C} \] \[ 2.33 \times 10^{2} \text{ N/C} \]

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by Brilliant Staff

Consider a solid sphere of radius \(a=2.30\text{ cm},\) which has a net uniform charge of \(q=+4.50\text{ fC}.\) What is the approximate magnitude of the electric field at radial distances (a) \(r=a/2\) and (b) \(r=a ?\)

The value of electrostatic constant is \(\displaystyle k=\frac{1}{4\pi\varepsilon_0}=8.99 \times 10^9 \text{ N}\cdot\text{m}^2\text{/C}^2.\)

\(\text{(a) } 1.91\times10^{-2}\text{ N/C},\text{ (b) } 0.076\text{ N/C} \) \(\text{(a) } 3.82\times10^{-2}\text{ N/C},\text{ (b) } 0.153\text{ N/C} \) \(\text{(a) } 3.82\times10^{-2}\text{ N/C},\text{ (b) } 0.076\text{ N/C} \) \(\text{(a) } 1.91\times10^{-2}\text{ N/C},\text{ (b) } 0.153\text{ N/C} \)

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by Brilliant Staff

Consider a metal rod with radius of \(R_1=1.20\text{ mm}\) and length \(L=12.00\text{ m},\) which is inside a very thin coaxial metal cylinder with radius of \(R_2=10.0 R_1\) and length \(L,\) as shown in the above figure. If the net charge on the rod and on the cylinder is \(Q_1=+3.40 \times 10^{-12}\text{ C}\) and \(Q_2=-2.0 Q_1,\) respectively, what is the approximate magnitude of the electric field at radial distance \(r=2.0 \times R_2,\) assuming that the charge density of both the rod and the cylinder are uniform?

The value of the permittivity constant is \(\varepsilon_0=8.85 \times 10^{-12} \text{ C}^2\text{/N}\cdot\text{m}^2.\)

\[ 0.848 \text{ N/C} \] \[ 0.636 \text{ N/C} \] \[ 0.212 \text{ N/C} \] \[ 0.424 \text{ N/C} \]

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by Brilliant Staff

Consider a Gaussian surface in the shape of a cube with edge length \(2.40\text{ m},\) as shown in the above figure. If the electric field in which the Gaussian surface lies can be expressed as \[\vec{E}=(2.00x+3.00)\hat{i}+5.00\hat{j}+6.00\hat{k} \text{ (N/C)},\] where \(x\) is in meters, what is the approximate net charge contained by the Gaussian surface?

The value of the permittivity constant is \(\varepsilon_0=8.85 \times 10^{-12} \text{ C}^2\text{/N}\cdot\text{m}^2.\)

\( 2.45 \times 10^{-10} \text{ C} \) \( 3.00 \times 10^{-10} \text{ C} \) \( 2.45 \times 10^{-11} \text{ C} \) \( 3.00 \times 10^{-11} \text{ C} \)

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by Brilliant Staff

Consider an infinitely large non-conducting plate of thickness \(d=9.20\text{ mm}.\) The above figure shows a cross section of the plate, where the origin of the \(x\)-axis is at the plate's center. If the plate has a uniform charge density of \(\rho=5.80\text{ fC/m}^3,\) what is the magnitude of the electric field at the \(x\)-coordinate of (a) \(4.60\text{ mm}\) and (b) \(27.0 \text{ mm}?\)

The value of the permittivity constant is \(\varepsilon_0=8.85 \times 10^{-12} \text{ C}^2\text{/N}\cdot\text{m}^2.\)

\(\text{(a) } 3.01\times10^{-6}\text{ N/C},\text{ (b) } 3.01\times10^{-6}\text{ N/C} \) \(\text{(a) } 6.03\times10^{-6}\text{ N/C},\text{ (b) } 6.03\times10^{-6}\text{ N/C} \) \(\text{(a) } 6.03\times10^{-6}\text{ N/C},\text{ (b) } 3.01\times10^{-6}\text{ N/C} \) \(\text{(a) } 3.01\times10^{-6}\text{ N/C},\text{ (b) } 6.03\times10^{-6}\text{ N/C} \)

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by Brilliant Staff

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Electric Flux

Concept Quizzes

Challenge Quizzes

Problem solving - Flux and Gauss' law

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.