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Chapter 17: Problem 60

A shark is able to detect the presence of electric fields as small as $1.0 \mu \mathrm{V} / \mathrm{m} .$ To get an idea of the magnitude of this field, suppose you have a parallel plate capacitor connected to a 1.5 - \(V\) battery. How far apart must the parallel plates be to have an electric field of $1.0 \mu \mathrm{V} / \mathrm{m}$ between the plates?

Short Answer

Expert verified
Answer: The distance between the parallel plates must be 1.5 x 10^6 meters.

Step by step solution

01

Write down the formula for electric field in a parallel plate capacitor

The electric field in a parallel plate capacitor can be calculated using the following formula: \(E = \frac{V}{d}\) where \(E\) is the electric field, \(V\) is the voltage, and \(d\) is the distance between the plates.
02

Plug in the given values

We are given the electric field \(E = 1.0 \mu \mathrm{V} / \mathrm{m}\) and the voltage \(V = 1.5 \, \mathrm{V}\). We can plug these values into the formula: \(1.0 \times 10^{-6} \, \mathrm{V/m} = \frac{1.5 \, \mathrm{V}}{d}\)
03

Solve for the distance \(d\)

Now we need to solve for \(d\): \(d = \frac{1.5 \, \mathrm{V}}{1.0 \times 10^{-6} \, \mathrm{V/m}}\)
04

Calculate the distance

Multiply both the numerator and denominator: \(d = \frac{1.5}{1.0 \times 10^{-6}} \, \mathrm{m}\) \(d = 1.5 \times 10^{6} \, \mathrm{m}\)
05

Write the final answer

The distance between the parallel plates must be \(1.5\times 10^{6}\) meters to have an electric field of \(1.0 \mu \mathrm{V/m}\).

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Most popular questions from this chapter

A capacitor can be made from two sheets of aluminum foil separated by a sheet of waxed paper. If the sheets of aluminum are \(0.30 \mathrm{m}\) by $0.40 \mathrm{m}$ and the waxed paper, of slightly larger dimensions, is of thickness \(0.030 \mathrm{mm}\) and dielectric constant \(\kappa=2.5,\) what is the capacitance of this capacitor?
A parallel plate capacitor is connected to a \(12-\mathrm{V}\) battery. While the battery remains connected, the plates are pushed together so the spacing is decreased. What is the effect on (a) the potential difference between the plates? (b) the electric field between the plates? (c) the magnitude of charge on the plates?
A van de Graaff generator has a metal sphere of radius \(15 \mathrm{cm} .\) To what potential can it be charged before the electric field at its surface exceeds \(3.0 \times 10^{6} \mathrm{N} / \mathrm{C}\) (which is sufficient to break down dry air and initiate a spark)?
The nucleus of a helium atom contains two protons that are approximately 1 fm apart. How much work must be done by an external agent to bring the two protons from an infinite separation to a separation of \(1.0 \mathrm{fm} ?\)
A defibrillator consists of a 15 - \(\mu\) F capacitor that is charged to $9.0 \mathrm{kV} .\( (a) If the capacitor is discharged in \)2.0 \mathrm{ms}$, how much charge passes through the body tissues? (b) What is the average power delivered to the tissues?
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