1.

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 isA. `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» Correct Answer - A
The electric potential due to charge `Q` is
`V = (1)/(4pi epsilon_(0)). (Q)/(r )` (i)
where `r` is the distance of observation point from the charge.
At the same point, electric field is
`E = (1)/(4pi epsilon_(0)).(Q)/(r )` (ii)
Combining Eqs. (i) and (ii), we have
`E = (4pi epsilon_(0)V^(2))/(Q) = (4pi epsilon_(0) xx (Q xx 10^(11))^(2))/(Q)`
`= 4pi epsilon_(0)Q xx 10^(22) V//m`


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