The electric potential at a certain point is given by V = -5.0z² + 2.0zy +7.0z, where V is in volts and a is in meters. What is the expression for the electric field at that point?

College Physics
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ISBN:9781305952300
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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The electric potential at a certain point is given by V = –5.0z² + 2.0zy + 7.0z, where V is
in volts and z is in meters. What is the expression for the electric field at that point?
Transcribed Image Text:The electric potential at a certain point is given by V = –5.0z² + 2.0zy + 7.0z, where V is in volts and z is in meters. What is the expression for the electric field at that point?
Expert Solution
Step 1

In this problem expression of electric potential is given as :

V = -5x² + 2xy + 7z 

We know, 

E = - [(δV/ δx) i + (δV/ δy) j  + (δV/ δz) k]       ------(1) 

Computing the derivative of 'V'

δV /δx = -10x 

δV /δy =2x

δV /δz = 7

Putting value of δV in above equation

E = - [  (-10x) i + (2x) j + 7 k ]

E = [(10x) i - (2x) j - 7k ] N/C

where i,j,k are unit vectors in x,y,z directions.

 

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