Chapter 6: Q14P (page 323)

Obtain Coulomb’s law from Gauss’s law by considering a spherical surface $δ$ with centre atq.

Short Answer

Expert verified

Coulomb's law is $E = \frac{q}{4 π ε_{0} r^{2}} \hat{R}$

Step by step solution

Given Information.

A Spherical surface $δ$ with centre atq.

Definition of Coulomb's law.

Coulomb's law states that the force of attraction between the two charged bodies which is directly proportional to the product of their charges or inversely proportional to the square of the distance between the two objects.

Use the Gauss's law.

Consider the Gauss's law $\oint E \cdot n d σ = \frac{q_{i n}}{ε_{0}} .$

Take the fiction closed surface to be a sphere surrounding the point charge of radius .

$E \cdot 4 π r^{2} = \frac{q_{i n}}{ε_{0}}$

Now, point radically outward the equation role="math" localid="1659183652852" $E \cdot = \frac{q_{i n}}{4 π r^{2} ε_{0}}$ .

Hence, Coulomb's law is $E \cdot = \frac{q_{i n}}{4 π r^{2} ε_{0} r^{2}} \hat{r}$

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Obtain Coulomb’s law from Gauss’s law by considering a spherical surface $δ$ with centre atq.

Short Answer

Step by step solution

Given Information.

Definition of Coulomb's law.

Use the Gauss's law.

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Obtain Coulomb’s law from Gauss’s law by considering a spherical surfaceδ with centre atq.

Short Answer

Step by step solution

Given Information.

Definition of Coulomb's law.

Use the Gauss's law.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Kinematics Physics

Further Mechanics and Thermal Physics

Mechanics and Materials

Electric Charge Field and Potential

Fields in Physics

Dynamics

Study anywhere. Anytime. Across all devices.

Obtain Coulomb’s law from Gauss’s law by considering a spherical surface $δ$ with centre atq.