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### College Physics (Urone)

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

# (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 $3.6×{10}^{12}N/C$ . (b) The field is too large to be in air. (c) 1.00 charge is excessive.

See the step by step solution

## 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,

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

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

role="math" localid="1653734461721"

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

## Step 4: (b) Unreasonable about the result

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

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.