A proton orbits a long charged wire, making 1.0 ×10^6 revolutions per second. The radies of the

step 1 Electric field for line charge is given by 2 lambda over r. So force is given by QE equals this

A proton orbits a long charged wire, making 1.0 ×10^6...

Key Concepts

Coulomb Force on a Charged Particle

A charged particle placed in an electric field experiences a force determined by Coulomb’s law, F = qE, where q is the charge of the particle and E is the electric field strength. This force calculation is critical when determining how electric fields influence the motion of charged particles.

Relation Between Revolution Frequency and Tangential Velocity

In uniform circular motion, the tangential velocity of a particle is directly related to its revolution frequency by the equation v = 2?rf, where r is the radius of the orbit and f is the frequency of revolutions per second. This relation allows one to convert rotational frequency into linear speed, which is useful when applying the centripetal force formula.

Electric Field from a Line Charge

An infinitely long charged wire creates an electric field that decreases with distance from the wire. According to Gauss's law, the magnitude of this field is given by E = ?/(2???r), where ? is the linear charge density, ?? is the vacuum permittivity, and r is the radial distance from the wire. This concept is fundamental to understanding how distributed charge produces fields in space.

Centripetal Force in Circular Motion

When a particle moves in a circular path, it experiences a centripetal force that keeps it in that path, given by F = m(v²/r), where m is the mass, v is the tangential velocity, and r is the radius of the circle. This force is always directed towards the center of the circle and is essential for analyzing rotational dynamics.

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