Some planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of −3.63×1016-3.63\$$times10^{16}$$−3.63×1016 Nm2/C at the planet's surface. Calculate the electric field at the planet's surface (refer to the astronomical data inside the back cover).

Ch 22: Gauss' Law

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

All textbooks

Young & Freedman Calc 14th Edition

Ch 22: Gauss' Law

Problem 16b

Chapter 22, Problem 16b

Some planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of $-3.63$\times$10^{16}$ Nm²/C at the planet's surface. Calculate the electric field at the planet's surface (refer to the astronomical data inside the back cover).

Verified step by step guidance

Understand the relationship between electric flux (Φ) and electric field (E). The electric flux through a closed surface is given by Gauss's Law: Φ = E * A, where A is the area of the surface.

Recognize that the electric flux (Φ) is given as -3.63×10^16 N·m²/C. This negative sign indicates the direction of the electric field lines is inward, towards the planet.

To find the electric field (E), rearrange Gauss's Law to solve for E: E = Φ / A.

Determine the surface area (A) of Mars. Use the formula for the surface area of a sphere: A = 4 * π * R², where R is the radius of Mars. Refer to astronomical data for the radius of Mars.

Substitute the values of Φ and A into the equation E = Φ / A to calculate the electric field at the planet's surface. Ensure units are consistent to obtain E in N/C.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electric Flux

Electric flux is a measure of the electric field passing through a given area. It is calculated as the product of the electric field and the area perpendicular to the field lines. In this context, the net electric flux is given, which helps in determining the electric field at Mars' surface using Gauss's Law.

Gauss's Law

Gauss's Law relates the electric flux through a closed surface to the charge enclosed by that surface. It states that the total electric flux is equal to the enclosed charge divided by the permittivity of free space. This principle is crucial for calculating the electric field at Mars' surface from the given electric flux.

Electric Field

The electric field is a vector field representing the force exerted per unit charge at any point in space. It is calculated from the electric flux using Gauss's Law, which allows us to determine the magnitude and direction of the field at the surface of Mars, given the net electric flux value.

Recommended video:

Guided course

03:16

Intro to Electric Fields

Related Practice

Textbook Question

The nuclei of large atoms, such as uranium, with $92$ protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately $7.4$\times$10^{-15}$ m. The electrons can be modeled as forming a uniform shell of negative charge. What net electric field do they produce at the location of the nucleus?

3138

views

Textbook Question

The nuclei of large atoms, such as uranium, with $92$ protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately $7.4 \times 10^{- 15}$ m. What is the electric field this nucleus produces just outside its surface?

A hollow, conducting sphere with an outer radius of $0.250$ m and an inner radius of $0.200$ m has a uniform surface charge density of $+ 6.37 \times 10^{- 6}$ C/m². A charge of $negative 0.500$ $μ$ C is now introduced at the center of the cavity inside the sphere. What is the new charge density on the outside of the sphere?

1998

views

Textbook Question

A very long uniform line of charge has charge per unit length $4.80$ $μ$ C/m and lies along the $x$ -axis. A second long uniform line of charge has charge per unit length $negative 2.40$ $μ$ C/m and is parallel to the $x$ -axis at $y equals 0.400$ m. What is the net electric field (magnitude and direction) at the following points on the $y$ -axis: (a) $y equals 0.200$ m and (b) $y equals 0.600$ m?

340

views

Textbook Question

Some planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of $-3.63$\times$10^{16}$ Nm²/C at the planet's surface. Calculate the charge density on Mars, assuming all the charge is uniformly distributed over the planet's surface.

Some planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of $- 3.63 \times 10^{16}$ Nm²/C at the planet's surface. Calculate the total electric charge on the planet.

1598

views

rank