E = x i ^ + y j ^ + z k ^ exists in space then choose incorrect statement(s) :

∇ × E = i ^ ∂ x ∂ x j ^ ∂ y ∂ y k ^ ∂ z ∂ z = 0 ∇ ⋅ E = ∂ x ∂ ( x ) + ∂ y ∂ ( y ) + ∂ z ∂ ( z ) = 1 + 1 + 1 = 3 Q e n c = ϵ 0 ∮ E ⋅ d A = ρ × V o l u m e = ( 3 ϵ 0 ) × ( 3 4 π ( 1 ) 3 ) = 4 π ϵ 0

Physics - Electrostatics Question with Solution | TestHub

PhysicsElectrostaticsElectric Field & ForceEasy2 minQB

PhysicsEasymultiple choice

$E = x \hat{i} + y \hat{j} + z \hat{k}$ exists in space then choose incorrect statement(s) :

Options:(select one or more)

Answer:

A, B, C

Solution:

$\nabla \times E = \hat{i} \frac{\partial}{\partial x} x \hat{j} \frac{\partial}{\partial y} y \hat{k} \frac{\partial}{\partial z} z = 0$

$\nabla \cdot E = \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial y} (y) + \frac{\partial}{\partial z} (z) = 1 + 1 + 1 = 3$

$Q_{e n c} = ϵ_{0} \oint E \cdot d A = ρ \times V o l u m e = (3 ϵ_{0}) \times (\frac{4}{3} π (1)^{3}) = 4 π ϵ_{0}$

Stream:JEESubject:PhysicsTopic:ElectrostaticsSubtopic:Electric Field & Force

⏱ 2mℹ️ Source: QB

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