The electric potential at a point in free space due to a charge `Q` coulomb is `Q xx 10^(11)` volts. The electric field at that point is

Options

A. `12 pi epsilon_(0)Qxx10^(22)` volt/m
B. `4piepsilon_(0)Qxx10^(22)` volt/m
C. `12pi epsilon_(0)Qxx10^(20)` volt /m
D. `4piepsilon_(0)Qxx10^(20)`volt/m

Answer

B

Explanation

Here `V=Q/(4 pi epsilon_(0)r)=Qxx10^(11)`
`:.4 pi epsilon_(0)r=10^(-11)`
Now `E=Q/(4 pi epsilon_(0)r^(2))=(Qxx4pi epsilon_(0))/((4pi epsilon_(0)r)^(2))`
`=(4 pi epsilon_(0)Q)/((10^(-11))^(2))=4 pi epsilon_(0)Qxx10^(22)V//m`