Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

Explain in your own words why equipotential lines and surfaces must be perpendicular to electric field lines.

As the work done in moving a charge on an equipotential surface is zero but the electric field and charge is non zero, the electric field must be perpendicular to the direction of motion of charge.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Definition of Equipotential surface

On the equipotential surface, the potential has the same value at every point. The equipotential lines are 2-D manifestations of the surfaces, on which potential is the same all along the line.

Step 2: Explanation of why equipotential lines and surfaces must be perpendicular to electric field lines

The work required (W) to move a charge along an equipotential line is zero;

$\begin{array}{rcl} W & = & - q \times dV \\ = & - q \times (0) \\ = & 0 \end{array}$

where q is electric charge and dv is potential difference.

This work is related to the electric field as:

$\begin{array}{rcl} W & = & F_{e} \times d \times cosθ \\ = & qE \times d \times cosθ \end{array}$

where F_e = qE is the force on charge q due to electric field E .

Since neither charge q nor electric field strength E is zero, $\cos (θ)$ must be zero.

Hence, $θ$ must be $90 °$ .

This means that the equipotential lines and surfaces are perpendicular to the electrical field lines.

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College Physics (Urone)

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Short Answer

Explain in your own words why equipotential lines and surfaces must be perpendicular to electric field lines.

Step by Step Solution

Step 1: Definition of Equipotential surface

Step 2: Explanation of why equipotential lines and surfaces must be perpendicular to electric field lines

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College Physics (Urone)

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Short Answer

Explain in your own words why equipotential lines and surfaces must be perpendicular to electric field lines.

Step by Step Solution

Step 1: Definition of Equipotential surface

Step 2: Explanation of why equipotential lines and surfaces must be perpendicular to electric field lines

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