In a certain region of space, the electric potential is V ( x , y , z )= A x y ?

Question

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.

Part A

Calculate the x-component of the electric field.

Express your answer in terms of the given quantities.

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Part B

Calculate the y-component of the electric field.

Express your answer in terms of the given quantities.

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Part C

Calculate the z-component of the electric field.

Express your answer in terms of the given quantities.

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Part D

At which point is the electric field equal to zero?

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.

Part A

Calculate the x-component of the electric field.

Express your answer in terms of the given quantities.

Ex =

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Part B

Calculate the y-component of the electric field.

Express your answer in terms of the given quantities.

Ey =

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Part C

Calculate the z-component of the electric field.

Express your answer in terms of the given quantities.

Ez =

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Part D

At which point is the electric field equal to zero?

At which point is the electric field equal to zero? x=0,y=0,z=0 x=?C/A,y=0,z=?2BC/A2 x=?C/A,y=?2BC/A2,z=C/A

Explanation / Answer

Calculate the -component of the electric field

Ex= -Ay+2Bx

Calculate the -component of the electric field.

Ey= -Ax-C

Calculate the -component of the electric field

Ex=0

At which point is the electric field equal to zero?

X=-C/A ,y=-2BC/A^@ , Z= C/

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