The electric potential at a point in free space due to a charge Q coulomb is `Qxx10^(11)` V. The electric field at that point is

Options

A. `4 pi epsilon_(0) Q xx 10^(22) V//m`
B. `12 pi epsilon_(0)Q xx 10^(20) V//m`
C. `4 pi epsilon_(0) Q xx 10^(20) V//m`
D. `12 pi epsilon_(0) Q xx 10^(22) V//m`

Answer

A

Explanation

Search for the relations of electric potential and electric field at a particular point At ant point, electric potential due to charge Q is
`V = (1)/(4 pi epsilon_90).(Q)/(r)`....(i)
where r is the distance of observation point from the charge.
At the same point electric field is
`E=(1)/(4 pi epsilon_(0)).(Q)/(r^(2))`....(ii)
Combining Eqs (i) and (ii), we have
`=(4 pi epsilon_(0)V^(2))/(Q) =(4 pi epsilon_(0)xx(Q xx10^(11))^(2))/(Q)`
`=4 pi epsilon_(0)Q xx 10_(22) V//m`