An electric field `E = (20hati + 30 hatj)` N/C exists in the space. If thepotential at the origin is taken be zero, find the potential at `(2 m, 2 m)`.

Options

A. `-50 V`
B. `100 V`
C. `-100 V`
D. `200 V`

Answer

3

Explanation

`V_(2) - V_(1) = -int_(r_(1))^(r_(2)) vec(E ) . d vec(r ) = -[ int_(x_(1)) ^(x_(2)) E_(x) dx + int_(y_(1)) ^(y_(2)) E_(y) dy]`
`V(2 ,2) - V(0,0) = [ int_(0)^(2) 20 dx + int_(0)^(2) 30 dy]`
`V_(2 ,3) - 0 -[ 20 xx 2 + 30 xx2 ] = - 100`
`V_(2 , 2) = - 100 V`