Chapter 4: Q7E (page 777)

Two protons, starting several meters apart, are aimed directly at each other with speeds of $2.00 \times 10^{5} \frac{m}{s}$ , measured relative to the earth. Find the maximum electric force that these protons will exert on each other.

Short Answer

Expert verified

The maximum electric force is $0.194 \times 10^{- 4} N$ that these protons will exert on each other.

Step by step solution

Electric force

The electric force between two protons is as follows:

$F = \frac{1}{4 {ττε}_{0}} \frac{| q_{1} q_{2} |}{r_{b}^{2}}$

The electric force acting of protons is derived as follows:

role="math" localid="1664256985484" $F = \frac{1}{4 π ε_{0}} \frac{| q_{1} q_{2} |}{r_{b}^{2}}$

$F = \frac{1}{4 {ττε}_{0}} \frac{| q_{1} q_{2} |}{r_{b}^{2}}$

Here,role="math" localid="1664256998618" $\frac{1}{4 π ε_{0}} \times 9 \times 10^{9} \frac{N . m^{2}}{C^{2}}$

Determine the value of electric force

Consider the charge of the proton is $1.602 \times 10^{- 19} C$ .

Consider the total kinetic energy for those two particles are equal.

$2 (\frac{1}{2} m v^{2}) = \frac{1}{4 π ε_{0}} \frac{|e^{2}|}{r_{b}} r_{b} = \frac{1}{4 π ε_{0}} \frac{e^{2}}{m v^{2}}$

Substitute the values and solve as:

$r_{b} = (9 \times 10^{9} \frac{N . m^{2}}{C^{2}}) \frac{{(1.602 \times 10^{- 19} C)}^{2}}{(1.67 \times 10^{- 27} kg) {(2 \times 10^{5} \frac{m}{s})}^{2}} = 3.45 \times 10^{- 12} m,$

Solve for the maximum force as:

$F = \frac{1}{4 {πε}_{0}} \frac{|e^{2}|}{r_{b}^{2}} = (9 \times 10^{9} \frac{N . m^{2}}{C^{2}}) \frac{{(1.607 \times 10^{- 19} C)}^{2}}{{(3.45 \times 10^{- 12} m)}^{2}} = 0.194 \times 10^{- 4} N$

Therefore, the maximum electric force is $0.194 \times 10^{- 4} N$ that these protons will exert on each other.

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Two protons, starting several meters apart, are aimed directly at each other with speeds of $2.00 \times 10^{5} \frac{m}{s}$ , measured relative to the earth. Find the maximum electric force that these protons will exert on each other.

Short Answer

Step by step solution

Electric force

Determine the value of electric force

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Two protons, starting several meters apart, are aimed directly at each other with speeds of 2.00×105ms, measured relative to the earth. Find the maximum electric force that these protons will exert on each other.

Short Answer

Step by step solution

Electric force

Determine the value of electric force

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism

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Study anywhere. Anytime. Across all devices.

Two protons, starting several meters apart, are aimed directly at each other with speeds of $2.00 \times 10^{5} \frac{m}{s}$ , measured relative to the earth. Find the maximum electric force that these protons will exert on each other.