An infinitely long line of charge has linear charge density 5.00×10−125.00\$$times10^{-12} C/m. A $$proton (mass 1.67×10−271.67\$$times10^{-27} kg$$, charge +1.60×10−19+1.60\$$times10^{-19} C) is 18.018.0 cm $$from the line and moving directly toward the line at 3.50×1033.50\$$times10^3 m/s. $$Calculate the proton's initial kinetic energy.

First, understand that kinetic energy (KE) is given by the formula: KE=12mv2, where m is the mass of the proton and v is its velocity. Identify the given values: the mass of the proton m=1.67×10-27 kg and its velocity v=3.50×103 m/s. Substitute these values into the kinetic energy formula: KE=12×1.67×10-27 kg × 3.50×1032 m/s. Calculate the square of the velocity: 3.50×1032 m/s. Multiply the mass by the squared velocity and then by 12 to find the initial kinetic energy of the proton.

Ch 23: Electric Potential

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

All textbooks

Young & Freedman Calc 15th Edition

Ch 23: Electric Potential

Problem 32a

Chapter 23, Problem 32a

An infinitely long line of charge has linear charge density $5.00 \times 10^{- 12}$ C/m. A proton (mass $1.67 \times 10^{- 27}$ kg, charge $+ 1.60 \times 10^{- 19}$ C) is $18.0$ cm from the line and moving directly toward the line at $3.50 times 10 cubed$ m/s. Calculate the proton's initial kinetic energy.

Verified step by step guidance

First, understand that kinetic energy (KE) is given by the formula:

K E = \frac{1}{2} m v^{2}

, where

m

is the mass of the proton and

v

is its velocity.

Identify the given values: the mass of the proton

m = 1.67 \times 10^{- 27}

kg and its velocity

v = 3.50 \times 10^{3}

m/s.

Substitute these values into the kinetic energy formula:

K E = \frac{1}{2} \times 1.67 \times 10^{- 27}

kg × 3.50×1032 m/s.

Calculate the square of the velocity:

{3.50 \times 10^{3}}^{2}

m/s.

Multiply the mass by the squared velocity and then by

\frac{1}{2}

to find the initial kinetic energy of the proton.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Linear Charge Density

Linear charge density is a measure of electric charge per unit length along a line. It is denoted by λ and is expressed in coulombs per meter (C/m). In this problem, the linear charge density helps determine the electric field generated by the infinitely long line of charge, which influences the motion of the proton.

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion, calculated using the formula KE = 0.5 * m * v^2, where m is the mass and v is the velocity of the object. For the proton in this problem, its initial kinetic energy is determined by its mass and initial velocity as it moves toward the line of charge.

Electric Field of an Infinite Line of Charge

The electric field generated by an infinitely long line of charge is uniform and radial, decreasing with distance from the line. It is calculated using the formula E = (λ / (2πε₀r)), where λ is the linear charge density, ε₀ is the permittivity of free space, and r is the distance from the line. This field affects the proton's motion and energy as it approaches the line.

Recommended video:

Guided course

08:20

Electric Field Lines

Related Practice

Textbook Question

A very long insulating cylinder of charge of radius $2.50$ cm carries a uniform linear density of $15.0$ nC/m. If you put one probe of a voltmeter at the surface, how far from the surface must the other probe be placed so that the voltmeter reads $175$ V?

views

Textbook Question

Two large, parallel conducting plates carrying opposite charges of equal magnitude are separated by $2.20$ cm. If the surface charge density for each plate has magnitude $47.0$ nC/m², what is the magnitude of $E$ in the region between the plates?

views

Textbook Question

A thin spherical shell with radius $R sub 1 equals 3.00$ cm is concentric with a larger thin spherical shell with radius $R sub 2 equals 5.00$ cm. Both shells are made of insulating material. The smaller shell has charge $q sub 1 equals positive 6.00$ nC distributed uniformly over its surface, and the larger shell has charge $q_{2} = - 9.00$ nC distributed uniformly over its surface. Take the electric potential to be zero at an infinite distance from both shells. What is the electric potential due to the two shells at the following distance from their common center: (i) $r equals 0$ ; (ii) $r equals 4.00$ cm; (iii) $r equals 6.00$ cm?

views

Textbook Question

At a certain distance from a point charge, the potential and electric-field magnitude due to that charge are $4.98$ V and $16.2$ V/m, respectively. (Take $V equals 0$ at infinity.) What is the magnitude of the charge?

views

Textbook Question

At a certain distance from a point charge, the potential and electric-field magnitude due to that charge are $4.98$ V and $16.2$ V/m, respectively. (Take $V = 0$ at infinity.) Is the electric field directed toward or away from the point charge?

Textbook Question

An infinitely long line of charge has linear charge density $5.00$\times$10^{-12}$ C/m. A proton (mass $1.67$\times$10^{-27}$ kg, charge $+1.60$\times$10^{-19}$ C) is $18.0$ cm from the line and moving directly toward the line at $3.50$\times$10^3$ m/s. How close does the proton get to the line of charge?

views