Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

A charge of $1.50 \times 10^{- 8} C$ lies on an isolated metal sphere of radius 16.0 cm. With $V = 0$ at infinity, what is the electric potential at points on the sphere’s surface?

The electric potential at points on the sphere’s surface is $V = 844 V$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data:

For the isolated metal sphere:

The radius, $R = 16.0 cm$

The value of the charge $q = 1.50 \times 10^{- 8} C$

At infinity, $V = 0$

Step 2: Determining the concept:

Use the equation of the electric potential at points on the sphere’s surface.

The electric potential is defined as the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in an electric field.

Formula:

The electric potential is define by,

$\begin{array}{rcl} V & = & \frac{1}{4 {πε}_{0}} \frac{q}{R} \\ = & k \frac{q}{R} \end{array}$

Here, V is electric potential, R is distance between the point charges, q is charge, $ε_{0}$ is the permittivity of free space, and k is the Coulomb’s constant having a value $9 \times 10^{9} N . m^{2} / C^{2}$ .

Step 3: Determining the electric potential on the sphere’s surface:

The electric potential on the sphere is,

$\begin{array}{rcl} V & = & \frac{1}{4 {πε}_{0}} \frac{q}{R} \\ = & k \frac{q}{R} \end{array}$

Substitute known values in the above equation.

$\begin{array}{rcl} V & = & 9.0 \times 10^{9} \times \frac{1.5 \times 10^{- 8}}{0.16} \\ = & 843.7 volts \\ \approx & 844 volts \end{array}$

Hence, the electric potential at points on the sphere’s surface is 844 V.

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Fundamentals Of Physics

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Short Answer

A charge of $1.50 \times 10^{- 8} C$ lies on an isolated metal sphere of radius 16.0 cm. With $V = 0$ at infinity, what is the electric potential at points on the sphere’s surface?

Step by Step Solution

Step 1: Given data:

Step 2: Determining the concept:

Step 3: Determining the electric potential on the sphere’s surface:

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Fundamentals Of Physics

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Short Answer

A charge of 1.50×10-8 C lies on an isolated metal sphere of radius 16.0 cm. With V=0 at infinity, what is the electric potential at points on the sphere’s surface?

Step by Step Solution

Step 1: Given data:

Step 2: Determining the concept:

Step 3: Determining the electric potential on the sphere’s surface:

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A charge of $1.50 \times 10^{- 8} C$ lies on an isolated metal sphere of radius 16.0 cm. With $V = 0$ at infinity, what is the electric potential at points on the sphere’s surface?