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Standard XII

Physics

Electric Field Due to Charge Distributions - Approach

In a certain ...

Question

In a certain region the electric potential at a point $(x, y, z)$ is given by the potential function $V = 2 x + 3 y - z$ . Then the electric field in this region will :

increase with increase in x and y

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increase with increase in y and z

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increase with increase in z and x

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remain constant

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Solution

The correct option is D remain constant

$V = 2 x + 3 y - z$

$E_{x} = - \frac{d V}{d x} = - 2, E_{y} = - \frac{d V}{d y} = - 3$ and $E_{z} = - \frac{d V}{d z} = 1$

As the field components are independent of x,y and z so the field remains constant.

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In a certain region the electric potential at a point (x,y,z) is given by the potential function V=2x+3y−z. Then the electric field in this region will :

The correct option is D remain constant V=2x+3y−z Ex=−dVdx=−2,Ey=−dVdy=−3 and Ez=−dVdz=1 As the field components are independent of x,y and z so the field remains constant.

In a certain region the electric potential at a point $(x, y, z)$ is given by the potential function $V = 2 x + 3 y - z$ . Then the electric field in this region will :

The correct option is D remain constant

$V = 2 x + 3 y - z$

$E_{x} = - \frac{d V}{d x} = - 2, E_{y} = - \frac{d V}{d y} = - 3$ and $E_{z} = - \frac{d V}{d z} = 1$

As the field components are independent of x,y and z so the field remains constant.