A charged capacitor produces a uniform field in frame

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Relativity & Gravitation · Relativistic dynamics and fields in flat spacetime

The Geometry of Gravity, Ch Tensors in flat spacetime: index notation and covariant field equations

Problem

A charged capacitor produces a uniform field

E_y = 2.0\times10^3\ \mathrm{V\,m^{-1}}

in frame

S

, with

\vec B = 0

throughout. An observer moves along

x

at constant speed

v

relative to

S

. Using the field-strength tensor's transformation law,

E_y' = \gamma(E_y - vB_z)

and

B_z' = \gamma(B_z - vE_y/c^2)

, with

c = 3.00\times10^8\ \mathrm{m\,s^{-1}}

: ((a)) Compute

E_y'

and

B_z'

for

v = 0.1c

v = 0.5c

, and

v = 0.9c

. ((b)) Show that the ratio

cB_z'/E_y'

depends only on

v/c

, and state that dependence.

Related theory

Relativistic electrodynamics

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