Chapter 23: Q. 50 (page 655)

A sphere of radius $R$ and surface charge density $η$ is positioned with its center distance $2 R$ from an infinite plane with surface charge density $η$ . At what distance from the plane, along a line toward the center of the sphere, is the electric field zero?

Short Answer

Expert verified

Distance from the plane along a line towards the center of the sphere, $d = R (2 - \sqrt{2})$

Step by step solution

Surface Charge Density

The quantity of charge per unit surface, measured in coulombs per sq meter, at every point on a surface charge distribution on a two-dimensional surface is known as surface charge density.

Find Surface density

We have such a distance from the plane along a line that leads to the sphere's center.

Assumed values:

We know that the sphere's charge is determined by,

$η = \frac{Q}{A}$

First, we must determine the value of $Q$ using the preceding formula.:

$η = \frac{Q}{A}$

$A$ is the sphere's area.

$Q = A \times η$

$Q = 4 π R^{2} η$

Changing the value of $A$ in the equation

We now have the distance $r$ :

$E_{s} + E_{p} = 0$

$\frac{1}{4 π ε_{o}} \frac{Q}{r^{2}} - \frac{η}{2 ε_{o}} = 0$

$\frac{1}{4 π ε_{o}} \frac{Q}{r^{2}} = \frac{η}{2 ε_{o}}$

Substitute a different value for $Q$ .

$\frac{1}{4 π ε_{o}} \frac{4 π R^{2} η}{r^{2}} = \frac{η}{2 ε_{o}}$

$\frac{R^{2}}{r^{2}} = \frac{1}{2}$

$r^{2} = 2 R^{2}$

$\Rightarrow r = \sqrt{2} R$

Find Distance from the plane along a line towards the center of the sphere

Distance from radius is,

$d = 2 R - r$

Substitute all values,

we get,

$d = 2 R - \sqrt{2} R$

$d = R (2 - \sqrt{2})$

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A sphere of radius $R$ and surface charge density $η$ is positioned with its center distance $2 R$ from an infinite plane with surface charge density $η$ . At what distance from the plane, along a line toward the center of the sphere, is the electric field zero?

Short Answer

Step by step solution

Surface Charge Density

Find Surface density

Find Distance from the plane along a line towards the center of the sphere

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A sphere of radius Rand surface charge density ηis positioned with its center distance 2R from an infinite plane with surface charge density η. At what distance from the plane, along a line toward the center of the sphere, is the electric field zero?

Short Answer

Step by step solution

Surface Charge Density

Find Surface density

Find Distance from the plane along a line towards the center of the sphere

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Thermodynamics

Electromagnetism

Conservation of Energy and Momentum

Electrostatics

Force

Turning Points in Physics

Study anywhere. Anytime. Across all devices.

A sphere of radius $R$ and surface charge density $η$ is positioned with its center distance $2 R$ from an infinite plane with surface charge density $η$ . At what distance from the plane, along a line toward the center of the sphere, is the electric field zero?