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1. [8-pts] Consider the differential forms of Maxwell\'s equations OB Ot Ot 1. R

ID: 1780179 • Letter: 1

Question

1. [8-pts] Consider the differential forms of Maxwell's equations OB Ot Ot 1. Rewrite Maxwell's equations for the case of electrostatics 2. Rewrite Maxwell's equations for the special case of a vacuum 3. Briefly compare the two cases, pointing out physically important differences 2. [8-pts] Once you've rewritten Maxwell's equations for a vacuum, recall that those equations lead directly to wave solutions. Below is a figurel1 of an electromagnetic wave in a vacuum Note the geometric relationship between the electric and magnetic components of the wave. Using Maxwell's equations in a vacuum explain why the electric and magnetic field vectors are always at right angles. [Hint think about the right-hand rule

Explanation / Answer

1. given maxwell's equations

del . E = rho/eo

del . B = 0

del x E = -dB/dt

del x B = muo(J + eo*dE/dt)

now for electrostats the time derivatives electric field and magnetic flux become zero

hence the maxwell's equations become

del . E = rho/eo

del . B = 0

del x E = 0

del x B = muo*J

for free space in vaccum

there are no charges

hence

del . E = 0

del . B = 0

del x E = -dB/dt

del x B = dE/c^2*dt