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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

Field lines and field strength

Four charged particles are held on the same plane, as shown in the above figure. The respective charges of the particles are \(q_1=q_2=+5.0 \,\mu\text{C},\) \(q_3=+4.0 \,\mu\text{C},\) and \(q_4=-16.0 \,\mu\text{C},\) and the distance \(d\) in the figure is \(8.0 \text{ mm}.\) What is the magnitude of the net electric field at point \(P\) due to the four particles?

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

\[ 6.0 \times 10^{-4} \text{ N/C} \] \[ \text{zero} \] \[ 4.0 \times 10^{-6} \text{ N/C} \] \[ 3.0 \times 10^{-5} \text{ N/C} \]

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by Brilliant Staff

Four particles are at the corners of a square with side length \(a=5.00\text{ cm},\) as shown in the above figure. The respective charges of the particles are \(q_1=+12.0\text{ nC},\) \(q_2=-24.0\text{ nC},\) \(q_3=+24.0\text{ nC},\) and \(q_4=-12.0\text{ nC}.\) What are the magnitude and direction of the net electric field at the center of the square?

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

\( 1.73 \times 10^5\ \mathrm{N/C}\) pointing to the \(+y\) direction \( 1.22 \times 10^5\ \mathrm{N/C}\) pointing to the \(-y\) direction \( 1.22 \times 10^5\ \mathrm{N/C}\) pointing to the \(+y\) direction \( 1.73 \times 10^5\ \mathrm{N/C}\) pointing to the \(-y\) direction

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by Brilliant Staff

In the above figure, the separation of electric field lines on the left is twice the separation of those on the right. If the magnitude of the field at position A is \(70\text{ N/C},\) what is the magnitude of the field at position B?

\( 140\text{ N/C} \) \( 35\text{ N/C} \) \( 70\text{ N/C} \) \( 105\text{ N/C} \)

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Three charged particles are held on the \(xy\)-plane, as shown in the above figure. The distance denoted \(d\) in the figure is \(d=6.00\,\mu\text{m}.\) If the respective charges of the particles are \(q_1=q_2=+4e\) and \(q_3=+8e,\) what is the magnitude of the net electric field at point \(P\) due to the three charged particles?

The value of electrostatic constant is \(\displaystyle k=\frac{1}{4\pi\varepsilon_0}=8.99 \times 10^9 \text{ N}\cdot\text{m}^2\text{/C}^2\) and the elementary charge is \(e=1.60 \times 10^{-19}\text{ C}.\)

\( 319.6 \text{ N/C} \) \( 639.3 \text{ N/C} \) \( 479.5 \text{ N/C} \) \( 159.8 \text{ N/C} \)

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by Brilliant Staff

The figure above portrays the electric field produced by two positive-charged particles. Which of the following correctly lists the points A, B, C, and D in order of increasing electric field strength?

A-D-B-C B-C-D-A A-D-C-B C-A-D-B

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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

Field lines and field strength

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.