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

Answer

C

Explanation

Since
`V=(Q)/(4pi epsilon_(0)r) and E=(Q)/(4pi epsilon_(0)r^(2)), `
Given `V=Qxx10^(11)=Q 4pi epsilon_(0)r`
`rArr" "r=(1)/(4pi epsilon_(0)xx10^(11))`
`"i.e, "E=(V)/(r)`
`rArr" "E=(QV)/(r)=Qxx10^(11)xx4piepsilon_(0)xx10^(11)`
`=4pi epsilon_(0)Qxx10^(22)"volt m"^(-1)`