Question

If the potential of field depends on (x, y) co-ordinate as v = a(x^2 - y^2), then

(1)Electric field, = is -2a(xi - y)
(2)Electric field,
is 2a(xi + )
(3)Equation of electric field lines is xy = constant
(4)Equation of electric field lines is x^2 - y^2 = constant​

Answer 1

E  = - 2a( xi  -  yj )   if  the potential of field depends on (x, y) co-ordinate as v = a(x^2 - y^2),

Explanation:

E  = - dv/dx

v = a(x^2 - y^2),

=> E =  - ( ∂i/∂x  +  ∂j/∂y  +  ∂k/∂z) (a(x^2 - y^2))

=> E  = - { (∂i/∂x)a(x^2 - y^2) + (∂j/∂y)a(x^2 - y^2)  + (∂i/∂z)a(x^2 - y^2) }

=> E  = - { (2axi  -2ayj  + 0k }

=> E  = - 2a( xi  -  yj )

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