Question

PI is located at (-2,0,0) m. P2 IS located at (1,4,0) m. l ne voltage difference when moving Trom P1 to P2 IS Δ V-25 V. Wnlch of following uniform (constant direction and magnitude) electric fields could yield this voltage difference? Select all that are True. E = (-7x-1^-29 N/C 0 E = (-3x-49) N/C

Answer 1

The vector R joining P1 and P2 is given by

R = ( -2 - 1) i + ( 0-4) j = ( -3 ) i + (-4) j , where i , j and k are unit vectors along x,y and z axes

Potential difference = 25 V

So dot product of vectors E and R should be 25 V

if E = (-3) i + (- 4) j + 5 k

E.R = (-3) x (-3) + (-4) x (-4) = 25 V —— So this field gives potential difference of 25V

let us now consider E = -7 i - j - 2 j

E.R = -7 x -3 + (-1) x (-4) = 25V——- So this field also gives 25V

Note

let us now consider E = -9 i + i + j

E.R = -9 x -3 + 1 x (-4 ) = 31 Volts , so this E does not give required potential difference ( p.d)

let us lastly consider

E = -3 i -4 j

E.R = -3 x -3 + -4 x -4 = 25 Volts, thus this field also gives rise to 25 volts p.d

Note: the potential difference between two points does not depend on the path between the points, in this case for ease of calculation we considered a straight line joining two points, but if we draw any other path also potential difference will work out to be same.

Another lesson here is that different types of fields can give rise to same potential difference between two points.