- #1

ARoyC

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- Homework Statement
- An infinite rod of charge density λ lies parallel to the x-axis. A point charge q is stationary at a distance r from the rod. An observer is moving with a velocity -vx̂. What is the force on the point charge from that observer's frame?

- Relevant Equations
- F = F_E + F_B

B of an Infinitely Long Current carrying Wire = µI/2πr

F_B = q(vxB)

F_E = qE

E of an Infinitely Long Uniformly Charged Rod = λ/2πεr r̂

As the observer is moving, there will be a magnetic force.

Electric Field of the Rod = λ/2πεr

Electric Force on the Point Charge = qλ/2πεr

Magnetic Force on the Point Charge = q(vxB) = qvB

= µqλv²/2πr

Total Force = Electric Force + Magnetic Force

Electric Field of the Rod = λ/2πεr

*r̂*Electric Force on the Point Charge = qλ/2πεr

*r̂*Magnetic Force on the Point Charge = q(vxB) = qvB

*n̂*= qv(µI/2πr)*n̂*= qv(µλv/2πr)*n̂*= µqλv²/2πr

*n̂*Total Force = Electric Force + Magnetic Force