- #1

Joe D

- 9

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## Homework Statement

Find t(τ), x(τ), y(τ), z(τ) for constant electric field

**E**=E(sinθ

**x**+cosθ

**z)**and

**B**=B

**z**, and constant magnetic field where E,B, and θ are all constants.

I haven't seen this notation before, and I really just want to know what it means specifically. I know and up indice paired with a down indice essentially gives an inner product, but I don't really know what an up indice paired with an up indice gives me. So this is equation 12.32 in Jackson Electrodynamics that I'm trying to understand.

## Homework Equations

m(d

^{2}x

^{α}/dτ

^{2})=(e/c)(∂

^{α}A

^{β}-∂

^{β}A

^{α})(dx

_{β}/dτ)

## The Attempt at a Solution

Also, the 4 vector potential that I've already calculated is:

A

^{α}=(-E(xsinθ+zcosθ),-By,0,0) where E, B and θ are all constants.

or A

^{α}=(-E(xsinθ+zcosθ),0,Bx,0) I can't decide which one is more convenient.

I've attached an image of my best guess for what that equation means.

#### Attachments

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