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Q19.4-40PE

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Found in: Page 697

### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# Sketch the equipotential lines in the vicinity of two opposite charges, where the negative charge is three times as great in magnitude as the positive. See Figure $${\rm{19}}{\rm{.28}}$$ for a similar situation. Indicate the direction of increasing potential.

The direction of increasing potential will be from the point $$q1$$ to $$q2$$. As, the point $$q1$$ is more negative than $$q2$$. The electric field lines that begin on $$q2$$ ends on $$q1$$.

See the step by step solution

## Step 1: Given Data

The electric field lines near two charge are shown as:

## Step 2: Define Electric Field

The term "electric field" refers to a physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them.

## Step 3: Concepts and Principles

Electric field lines are represented with their corresponding electric field vectors $$\mathop {\rm{E}}\limits^ \to$$ tangent to the lines at all points along the lines.

Positively charged items have electric field lines that start there and terminate with negatively charged objects (these charged objects do not need to be present on the sketches).

A charged item's charge intensity is inversely correlated with the number of electric field lines at the beginning or end of that thing. Therefore, there will be twice as many electric field lines leaving a charge of $$+ 2q$$ and $$+ q$$ as there are electric field lines entering a charge of on an electric field diagram.

Therefore, the density of the electric field lines in a place is inversely related to the strength of the electric field there.

The lines do not cross; if they did, the force acting on a test charge positioned there would not be known.

The direction of the largest potential reduction is indicated by the electric field lines.

A surface on which the potential has a constant value throughout is said to be equipotential. Both are said to be perpendicular when a field line crosses an equipotential surface. The interior of a conductor's points are all at the same potential when all charges are at rest, and the surface of the conductor is always an equipotential surface. When a conductor's cavity is empty of charge, the whole cavity is an equipotential zone and the cavity's surface is devoid of all surface charges.

There is no surface charge present anywhere on the cavity's surface since it is an equipotential zone.

## Step 4: The required data

We are suppose to sketch the equipotential lines for two charges $$q1$$ and $$q2$$. The first one having a magnitude three times that of the positive one. Also, indicating the direction of increasing potential.

## Step 5: Sketching equipotential charges of both points and indication of their direction

The electric field for the given charge distribution is drawn. The equipotential lines are drawn perpendicular to the electric field lines. The sketch of the equipotential lines near the two charges is shown in the figure below as:

As, the point $$q1$$ is more negative than the point $$q2$$, the electric field lines that begin on the point $$q2$$ ends on the point $$q1$$. Hence, the direction of increasing potential will be from the point $$q1$$ to the point $$q2$$.

Therefore, The point $$q1$$ is more negative than $$q2$$. Then, the electric field lines that begin on $$q2$$ ends on $$q1$$. So, the direction of increasing potential will be from the point $$q1$$ to $$q2$$.