Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

(a) Calculate the electric field strength near a 10.0 cm diameter conducting sphere that has 1.00 C of excess charge on it. (b) What is unreasonable about this result? (c) Which assumptions are responsible?

(a) The strength of the electric field is $3.6 \times 10^{12} N / C$ . (b) The field is too large to be in air. (c) 1.00 charge is excessive.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Data

Diameter of a sphere is 10.0 cm

Charge on sphere is 1.00 C

Step 2: Electric field

The electric field is defined as the force experienced by a unit positive test charge due to the presence of another charge. The expression for the electric field is,

$E = \frac{F}{q_{\circ}}$

Here, F is the electrostatic force and $q_{\circ}$ is the test charge.

Step 3: (a) Strength of the electric field

The formula for electric field strength is,

$E = \frac{K q}{{(\frac{d}{2})}^{2}}$

Here, K is the electrostatic force constant, q is the charge on the conducting sphere, and d is the diameter of the sphere.

Substitute $K = 9 \times 10^{9} N - m^{2} / C^{2}, q = 1.00 C, d = 10.0 c m,$

role="math" localid="1653734461721" $E = \frac{(9 \times 10^{9} N - m^{2} / C^{2}) \times (1.00 C)}{{(\frac{10.0 c m}{2})}^{2}} = \frac{(9 \times 10^{9} N - m^{2} / C^{2}) \times (1.00 C)}{{[(\frac{10.0 c m}{2}) \times (\frac{10^{- 2} m}{1 c m})]}^{2}} = 3.6 \times 10^{12} N / C$

Hence, the value of the electric field strength is $3.6 \times 10^{12} N / C$ .

Step 4: (b) Unreasonable about the result

The dielectric breakdown occurs at $3 \times 10^{6} N / C$ , which is much less than the field outside this sphere. Sparks would occur before reaching the field strength of $3.6 \times 10^{12} N / C$ .

Hence, the field is too large to be in air.

Step 5: (c) Responsible assumptions

The responsible assumption is that, the 1.00 C charge is excessive.

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College Physics (Urone)

Answers without the blur.

Short Answer

(a) Calculate the electric field strength near a 10.0 cm diameter conducting sphere that has 1.00 C of excess charge on it. (b) What is unreasonable about this result? (c) Which assumptions are responsible?

Step by Step Solution

Step 1: Given Data

Step 2: Electric field

Step 3: (a) Strength of the electric field

Step 4: (b) Unreasonable about the result

Step 5: (c) Responsible assumptions

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College Physics (Urone)

Answers without the blur.

Short Answer

(a) Calculate the electric field strength near a 10.0 cm diameter conducting sphere that has 1.00 C of excess charge on it. (b) What is unreasonable about this result? (c) Which assumptions are responsible?

Step by Step Solution

Step 1: Given Data

Step 2: Electric field

Step 3: (a) Strength of the electric field

Step 4: (b) Unreasonable about the result

Step 5: (c) Responsible assumptions

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