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Chapter 20: Problem 27

A -1.0 - \(\mu\) C charge experiences a \(10 \hat{\imath}\) -N electric force in a certain electric field. What force would a proton experience in the same field?

Short Answer

Expert verified
The proton would experience an electric force of -1.6 x \(10^{-12}\) \(\hat{\imath}\) N in the same field.

Step by step solution

01

Identify Information Within the Problem

In the problem, it is given that the force experienced by a -1.0-\(\mu\)C charge in the electric field is \(10 \hat{\imath}\) N. We also know that the charge of a proton is \(+1.6 \times 10^{-19}\) C.
02

Determine the Magnitude of the Electric Field

Given the force and charge, the electric field strength experienced by -1.0-\(\mu\)C charge can be found using the equation \( E = F/q \), which yields an electric field of \( E = 10 / (-1.0 \times 10^{-6}) = -10^7 \hat{\imath} \) N/C.
03

Calculate the Force on a Proton

Using the same equation as before, we can now determine the force on the proton. Plugging in the values, it yields \( F = qE = (1.6 \times 10^{-19}) \times (-10^7 \hat{\imath}) = -1.6 \times 10^{-12}\) N, where the force is directed along the negative x-axis as indicated by '\(\hat{\imath}\)'.

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Most popular questions from this chapter

A typical lightning flash delivers about 25 C of negative charge from cloud to ground. How many electrons are involved?

Find the magnitude of the electric force on a 2.0 - \(\mu \mathrm{C}\) charge in a \(100-\mathrm{N} / \mathrm{C}\) electric field.

A \(9.5-\mu \mathrm{C}\) charge is at \(x=15 \mathrm{cm}, y=5.0 \mathrm{cm}\) and a \(-3.2-\mu \mathrm{C}\) charge is at \(x=4.4 \mathrm{cm}, y=11 \mathrm{cm} .\) Find the force on the negative charge.

You're \(1.44 \mathrm{m}\) from a charge distribution that is well under \(1 \mathrm{cm}\) in size. You measure an electric field strength of \(296 \mathrm{N} / \mathrm{C}\) due to this distribution. You then move to a distance of \(2.16 \mathrm{m}\) from the distribution, where you measure a field strength of \(87.7 \mathrm{N} / \mathrm{C}\) What's the net charge of the distribution? Hint: Don't try to calculate the charge. Determine instead how the field decreases with distance, and from that infer the charge.

A \(65-\mu \mathrm{C}\) point charge is at the origin. Find the electric field at the points (a) \(x=50 \mathrm{cm}, y=0 \mathrm{cm} ;\) (b) \(x=50 \mathrm{cm}, y=50 \mathrm{cm}\) and \((\mathrm{c}) x=25 \mathrm{cm}, y=-75 \mathrm{cm}\)
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