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An electric field E = (20hati + 30 hatj)...

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)`.

Text Solution

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`dV = -vec(E ).vec(dr) = -(20 hat(i) + 30 hat(j)).(dx hat(i) + dy hat(j))` or `dV= -20dx - 30dy`
Now we will have to integrate in within limits. Given V=0 when x= 0 and y=0 (lower limit) and we have to calaculate V when x=2 and y=2 (upper limit) Therefore
`underset(0)overset(V)int dV = -20 underset(x=0)overset(x=2)int dx =30 underset(y=0)overset(y=2)int dy`
`rArrV=-40 -60 = -100` volt.
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