Question

The electric potential in a region is given by V = 2.0xy - 3.0zx + 5.0y^2, with V in volts and the coordinates in meters. Part A Find the potential of the electric field at the point x = 3 m, y = 0 m, z = 1 m. Express your answer with the appropriate units. V = Value Units Part B Find the components of the electric field at the point x = 3 m, y = 0 m, z = 1 m. Enter your answers in volts per meter separated by commas. Ex, Ey, Ez = V/m

          The electric potential in a region is given by V = 2.0xy - 3.0zx + 5.0y^2, with V in volts and the coordinates in meters. 

Part A 
Find the potential of the electric field at the point x = 3 m, y = 0 m, z = 1 m. 
Express your answer with the appropriate units. 
V = Value Units 

Part B 
Find the components of the electric field at the point x = 3 m, y = 0 m, z = 1 m. 
Enter your answers in volts per meter separated by commas. 
Ex, Ey, Ez = V/m

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The electric potential in a region is given by V = 2.0xy - 3.0zx + 5.0y^2, with V in volts and the coordinates in meters.

Part A
Find the potential of the electric field at the point x = 3 m, y = 0 m, z = 1 m.
Express your answer with the appropriate units.
V = Value Units

Part B
Find the components of the electric field at the point x = 3 m, y = 0 m, z = 1 m.
Enter your answers in volts per meter separated by commas.
Ex, Ey, Ez = V/m

Added by Rachel F.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

05/12/2023

Step 1

We can do this by plugging in the coordinates into the given equation: V = 2.0rx + 3.0zt + 5.0y^2 V = 2.0(3)(0) + 3.0(1)(1) + 5.0(0)^2 V = 0 + 3 + 0 V = 3 V Now, we need to find the components of the electric field E at the same point. The electric field is Show more…

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The electric potential in a region is given by V = 2.0xy - 3.0zx + 5.0y^2, with V in volts and the coordinates in meters. Part A: Find the potential of the electric field at the point x = 3 m, y = 0 m, z = 1 m. Express your answer with the appropriate units. V = Part B: Find the components of the electric field at the point x = 3 m, y = 0 m, z = 1 m. Enter your answers in volts per meter separated by commas. Ex, Ey, Ez = V/m

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Transcript

00:01 Hi students, here in this question the potential is given as v is equal to 2xy -3xz plus 5y square.

00:11 Now we have to find out the potential at 3 ,0 ,1.

00:18 V at 3 ,0 ,1 that means x equal to 3, y is equal to 0, z is equal to 1.

00:27 X equal to 3, y is equal to 0, z is equal to 1.

00:31 So what will be v at 3 ,0 ,1 just substituting the values for x and y and z.

00:38 Okay, so 2 into 3 into 2 into 3 into 0 minus 3 into 1 into 3 plus 5 into 0 square.

00:56 So that's equal to minus 9 volt.

01:00 So this is v at minus 3 ,0 ,1.

01:07 Therefore potential difference at the point 3 ,0 ,1 is v is equal to minus 9 volt.

01:26 Now we have to find out the components of the electric field, ex, ey and ez.

01:33 So we know that e, e is nothing but minus del v.

01:42 So what is del v? so minus of dou v by dou x into i cap plus dou v by dou y into j cap plus dou v by dou z into k cap.

02:00 So that's equal to, here we can substitute the values.

02:05 Okay, so what is v? v is 2xy minus 3zx plus 5y square.

02:11 So we have to partially differentiate with respect to x, y and z.

02:16 Okay, so here it will be dou v by dou x.

02:22 So dou v by dou x 2y into 1 minus 3z into 1.

02:30 So it is 2y minus 3z into i cap.

02:36 Okay, minus of minus, minus of plus.

02:41 So it will be minus...

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