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PhysicsElectrostaticsRelation between field & potentialMedium2 minQB

PhysicsMediumsingle choice

In a certain region of space, the potential is given by : $V = k [2 x^{2} - y^{2} + z^{2}]$ . The electric field at the point (1, 1, 1) has magnitude =

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Ans (B)

$E = - \nabla V$

$= - [\hat{i} \frac{\partial}{\partial x} + \hat{j} \frac{\partial}{\partial y} + \hat{k} \frac{\partial}{\partial z}] [k (2 x^{2} - y^{2} + z^{2})]$

$= - k [4 x \hat{i} - 2 y \hat{j} + 2 z \hat{k}]$

$E_{(1, 1, 1)} = - k [4 \hat{i} - 2 \hat{j} + 2 \hat{k}]$

$∣ E ∣ = 2 k 4 + 1 + 1 = 26 k$

Stream:JEESubject:PhysicsTopic:ElectrostaticsSubtopic:Relation between field & potential

⏱ 2mℹ️ Source: QB

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