In a certain region of space, the electric potential is $V (x, y, z) = A x y - B x^{2}$ $+ C y$ , where $A, B a n d C$ are positive constants. Calculate the $x, y a n d z$ components of the electric field.

E_{x} = - A x, E_{y} = - A y, E_{z} = 0

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E_{x} = - A x + 2 B x, E_{y} = - A y - C, E_{z} = 0

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E_{x} = - A y + 2 B x, E_{y} = - A x - C, E_{z} = 0

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E_{x} = - A y, E_{y} = - A x, E_{z} = 0

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Solution

The correct option is C $E_{x} = - A y + 2 B x, E_{y} = - A x - C, E_{z} = 0$
Here, $V (x, y, z) = A x y - B x^{2} + C y$

So, $E_{x} = - \frac{V}{d x} = - [A y - 2 B x] = 2 B x - A y$ ;

$E_{y} = - \frac{d V}{d y} = - [A x + C] = - A x - C$ and

$E_{z} = - \frac{d V}{d z} = 0$

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In a certain region of space, the electric potential is V(x,y,z)=Axy−Bx2 +Cy, where A,B and C are positive constants. Calculate the x,y and z components of the electric field.

The correct option is C Ex=−Ay+2Bx,Ey=−Ax−C,Ez=0Here, V(x,y,z)=Axy−Bx2+CySo, Ex=−Vdx=−[Ay−2Bx]=2Bx−Ay;Ey=−dVdy=−[Ax+C]=−Ax−C and Ez=−dVdz=0

In a certain region of space, the electric potential is $V (x, y, z) = A x y - B x^{2}$ $+ C y$ , where $A, B a n d C$ are positive constants. Calculate the $x, y a n d z$ components of the electric field.

The correct option is C $E_{x} = - A y + 2 B x, E_{y} = - A x - C, E_{z} = 0$
Here, $V (x, y, z) = A x y - B x^{2} + C y$

So, $E_{x} = - \frac{V}{d x} = - [A y - 2 B x] = 2 B x - A y$ ;

$E_{y} = - \frac{d V}{d y} = - [A x + C] = - A x - C$ and

$E_{z} = - \frac{d V}{d z} = 0$