Electric Field Questions

An electron (mass $9\times 10^{-31}\text{kg}$ and charge $1.6\times 10^{-19}\text{C}$) moving with speed $c/100$ ($c$ = speed of light) is injected into a magnetic field $\vec{B}$ of magnitude $9\times 10^{-4}\text{T}$ perpendicular to its direction of motion. We wish to apply a uniform electric field $\vec{E}$ together with the magnetic field so that the electron does not deflect from its path. Then (speed of light $c=3\times 10^8{\text{ms}}^{-1}$):

The electric field in a plane electromagnetic wave is given by $E_z=60\cos (5x+1.5\times 10^{9}t)\text{ V/m}$. Then expression for the corresponding magnetic field is:

A conducting ring of radius $1\text{meter}$ is placed in a uniform magnetic field $B$ of $0.01\text{tesla}$ oscillating with frequency $100\text{Hz}$ with its plane at right angles to $B$. What will be the induced electric field?

Two infinitely long parallel conducting plates having surface charge densities $+\sigma$ and $-\sigma$ respectively, are separated by a small distance. The medium between the plates is vacuum. If ${\epsilon }_0$ is the dielectric permittivity of vacuum, then the electric field in the region between the plates is:

A thin conducting ring of radius $R$ is given a charge $+Q$. The electric field at the centre $O$ of the ring due to the charge on the part $AKB$ of the ring is $E$. The electric field at the centre due to the charge on the part $ACDB$ of the ring is: