InterviewSolution
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InterviewSolution
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If electric field is (a) vec E = 2 a x y hat(i) + a(x^(2) - y^(2)) hat(j) (b) vec(E ) = ay hat(i) + (ax + bz) hat(j) + by hat(k)) Find potential. |
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Answer» Solution :(a) `DV = -vec(E ). D vec(r ) = -(E_(X) dx + E_(y) dy)` `= - [2 a x y dx + a(x^(2) - y^(2))dy]` `= -[2a x y dx + AX^(2) y - ay^(2) dy]` `int 2a xy dx = 2ay int xdx = 2 ay (x^(2))/(2) = ax^(2) y` `int ax^(2) dy = ax^(2) int dy = ax^(2) y` `2 a x y dx + ax^(2) dy= d (ax^(2) y)` `V = - int vec(E ) . d vec(r ) = - int d(ax^(2) y) - a y^(2) dy` `= - [ ax^(2)y - (ay^(3))/(3)] + C` (b) `dV = -[aydx + (ax + BZ)dy + by DZ]` `= - [a(y dx + xdy) + b(zdy + ydz)]` `-[ad(xy) + bd(yz)]` `V = - int vec(E ) . d vec(r) = - [ int ad(xy) + bd(yz)]` `= -(axy + byz) + C` |
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