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 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Young & Freedman Calc 14th Edition

Ch 23: Electric Potential

문제 30a

23장, 문제 30a

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.

검증된 단계별 안내

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.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

관련 실천

교과서 질문

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?

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?

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?

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?

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?

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교과서 질문

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?

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