Electric potential and flux

Electricity and Magnetism Level 2

Electric potential at any point ( x , y , z ) (x, y, z) in the coordinate space is given by V = 4 x 2 − 3 x . V = 4x^2 -3x. Find the electric field at the point ( x , y , z ) . ( x, y, z ).

x ^ and y ^ \hat{ x } \text{ and } \hat{ y} unit vectors in the x x and y y directions, respectively.

− ( 8 x ) y ^ -(8x)\text{ } \hat{ y} − ( 8 x − 3 ) x ^ -(8x - 3)\text{ } \hat{ x} ( 8 x ) x ^ (8x) \text{ }\hat{ x} ( 8 x − 3 ) x ^ (8x - 3)\text{ } \hat{ x}

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Srinivasa Satti by Srinivasa Satti

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1 solution

− d V = E ⃗ ⋅ d s - dV = \vec{E} \cdot ds . Due to the electric potential has an only component − d V = E ⃗ ⋅ d s = E ⃗ ⋅ d x -dV =\vec{E} \cdot ds = \vec{E} \cdot dx ⇒ \Rightarrow E ⃗ = − d V d x = − ( 8 x − 3 ) x ^ \vec{E} = -\dfrac{dV}{dx} = - (8x -3) \hat x

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