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Chapter 20: Problem 25

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 force a proton would experience in the same field is -\(1.6 \times 10^{-12} \hat{\imath}\) N.

Step by step solution

01

Identify given quantities and formula

The question states that a -1.0 - \(\mu\) C charge experiences a \(10 \hat{\imath}\) -N force. The formula we are going to use is \(F = qE\), where F is the force, q is the charge, and E is the electric field strength.
02

Compute the electric field strength

First, the electric field strength can be determined by manipulating the formula to \(E = F/q\). Substituting in the given values gives \(E =10/-1\times10^{-6}\). This yields a value of \(-1 \times 10^{7} \hat{\imath}\) N/C.
03

Calculate force on proton

We now find the force on a proton using the same initial formula of \(F = qE\). Substituting the proton's charge of +\(1.6 × 10^{-19}\) C into the formula along with the computed electric field strength, we get \(F = 1.6 \times 10^{-19} \times -1 \times 10^{7}\). This yields as -\(1.6 \times 10^{-12} \hat{\imath}\) N as the force that a proton would experience in the same field.

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Most popular questions from this chapter

How strong an electric field is needed to accelerate electrons in an X-ray tube from rest to one-tenth the speed of light in a distance of \(5.0 \mathrm{cm} ?\)

Find the line charge density on a long wire if a 6.8 - \(\mu \mathrm{g}\) particle carrying 2.1 nC describes a circular orbit about the wire with speed \(280 \mathrm{m} / \mathrm{s}\)

Two identical small metal spheres initially carry charges \(q_{1}\) and \(q_{2} .\) When they're \(1.0 \mathrm{m}\) apart, they experience a \(2.5-\mathrm{N}\) attractive force. Then they're brought together so charge moves from one to the other until they have the same net charge. They're again placed \(1.0 \mathrm{m}\) apart, and now they repel with a \(2.5-\mathrm{N}\) force. What were the original charges \(q_{1}\) and \(q_{2} ?\)

An electron at Earth's surface experiences a gravitational force \(m_{c} g .\) How far away can a proton be and still produce the same force on the electron? (Your answer should show why gravity is unimportant on the molecular scale!)

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