A) The magnetic field doubles as well
The relationship between rms value of the electric field and rms value of the magnetic field for an electromagnetic wave is the following:
where
E_rms is the magnitude of the electric field
c is the speed of light
B_rms is the magnitude of the magnetic field
From the equation, we see that the electric field and the magnetic field are directly proportional: therefore, if the rms value of the electric field is doubled, then the rms value of the magnetic field will double as well.
B) The intensity will quadruple
The intensity of an electromagnetic wave is given by
where
c is the speed of light
is the vacuum permittivity
is the peak intensity of the electric field
The rms value of the electric field is related to the peak value by
So we can rewrite the equation for the intensity as
we see that the intensity is proportional to the square of the rms value of the electric field: therefore, if the rms value of the electric field is doubled, the average intensity of the wave will quadruple.