(a) How much work would it take to push two protons very slowly from a separation of 2.00 ×10^-1

(a) How much work would it take to push two protons very...

Key Concepts

Coulomb's Law

Coulomb's Law describes the electrostatic force between two point charges. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This fundamental relationship is essential for calculating the interactions between charged particles over various distances.

Electric Potential Energy

Electric potential energy represents the energy stored in a system of charges due to their positions relative to each other. In the context of charged particles, such as protons, the potential energy is determined by their magnitudes, separation distance, and the medium between them. This concept is critical for understanding how work done in moving charges changes the energy stored in the system.

Work-Energy Principle in Electrostatics

The work-energy principle in electrostatics relates the work done on charged particles to the change in their electric potential energy. When charges are moved slowly from one configuration to another, the external work done is equal to the difference in potential energy between the two configurations. This principle is important for analyzing energy transfer in systems involving electric forces.

Conservation of Energy

The conservation of energy principle states that the total energy in an isolated system remains constant. In problems involving electrostatic forces, it implies that any work done on a system (such as pushing charges together) is transformed into other forms of energy, like kinetic energy. This concept is key for understanding how the potential energy stored in a system converts into kinetic energy when constraints are removed.

Transcript

00:01 Hello friends here it is given how much work would it take so we have to require the work done to push two protons very slowly from separation so there is one proton plus e another proton is plus e initial separation between them is 2 into 10 to the power minus 10 meter now they are slowly pushed towards each other so that the the separation reduced to r2 and it is given 3 into 10 to the power of minus 15 meters.

01:07 So in the part a, we have to require the wogden.

01:10 In the part b, we have to calculate how fast, that is velocity, when passing through their original position.

01:38 Now basic concept of this solve, vodl done is called to change in potential energy of interaction work done is called to change in potential energy of interaction so we start solving now part a work done is called to final potential energy minus initial potential energy final is 1 upon 4 pi epsilon not q 1 q 2 by r so e into e upon r 2 r 2 1 upon 4 pi epsilon n e into e upon r1 now simplify it 1 upon 4 pi epsilon not into e square can be taken common 1 upon r2 minus 1 upon r 1 upon r 1 now simplify it 1 upon r 4 pi epsilon not 9 into 10 to the power 9 e is 1 .6 into 10 to the power of minus 19 column r2 is 3 into 10 to the power of minus 15 and r1 is 2 into 10 to the power of minus 15 on solving it work done will be 7 .68 into 10 to the power of minus 14 jule so this is the answer of first part now for second part b when they are released potential energy converts into kinetic energy will be when they are released potential energy converts into kinetic energy and other concepts since external force on the system is zero so momentum remain concerned initially both are at rest so initial momentum is zero their masses are same so they will move equal and opposed with the same speed that is b1 is called to v2 is called to b now change in potential energy is called to kinetic energy that already we have calculated 7 .68 into 10 to the power 40 is called to half mb square plus half mb square because both having the same speed opposite in direction so from here velocity will be root of 7 .68 into 10 to the power minus 14 divided by mass of proton 1 .67 into 10 to the power minus 27.

06:05 So its speed will be 6 .67 into 10 to the over 6 meter per second...

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