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Q. 35

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Found in: Page 654

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

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# What are the strength and direction of the electric field at the position indicated by the dot in FIGURE P? Give your answer (a) in component form and (b) as a magnitude and angle measured cw or ccw (specify which) from the positive -axis.

a. The electric field at the dot is .

b. The angle made by the electric filed is counter clockwise direction from the positive -axis.

See the step by step solution

## Step 1: Formula for electric field

The electric field is,

permittivity of free space is .

## Step 2: Diagram for electric field position

In the diagram below, two positive charges and one negative charge are located in the three corners of a rectangle.

The electric field generated by the positive charge at the dot is directed away from the positive charge. The electric field generated by the negative charge at the dot is directed towards the negative charge.

## Step 3: Explanation (part a)

a.

Calculate the component form of the electric field strength at the place given by the dot in the diagram.

The angle formed by the vertical and the diagonal is,

The component form of the resultant electric field at the dot is as follows:

From figure,

## Step 4: Explanation (part a) solution

a.

-component of the net electric field at the dot.

The magnitude of the electric field due to the charge one is

The magnitude of the electric field due to the charge two is,

The magnitude of the electric field due to the charge three is,

The value,

So,

## Step 6: Explanation (part a)

For component,

So,

So electric dot is,

## Step 7: Explanation (part b)

b.

Magnitude of the electric field at the dot is given by the expression,

Substitute all values,

## Step 8: Explanation part b

angle of electric field is,

Here, negative sign indicates counter clockwise direction from the positive-axis.

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