Question

Given the electrical potential in a region as V ( x , y ) = (
345^2+ 24510^3+4 ) V , find the x - component of the electric field
( in N / C ) at the point ( 45m , 0 , 0 )

Answer #1

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Potential should be given in terms of 'x' and 'y' where is it?

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The electric potential in a region is given by
V(x,y,z) = -10.0x2 + 20.0xyz + 6.0y3
a) Find the electric field that produces this potential?
b) Find the amount of charge contained within a cubic region in
space 20 cm on a side and centered at the point (10.0 cm, 10.0 cm,
10.0 cm).

Calculate the electrical potential at any point P = (x,y) due to
two electrical charges of 5C and 2C located at (0, 0) and (1, 0)
respectively and in particular when it is the electrical potential
at point (3, 4)? How much is the electric field at any point (x, y)
and in particular at (3, 4)?
Note: Write step by step

In a certain region of space the electric potential is
given by V=+Ax2y−Bxy2, where A =
5.00 V/m3 and B = 8.00 V/m3.
Calculate the magnitude of the electric field at the
point in the region that has cordinates x =
2.20 m, y = 0.400 m, and z =
0
Calculate the direction angle of the electric field at
the point in the region that has cordinates x =
2.20 m, y = 0.400 m, and z =
0.

Suppose that over a certain region of space the electrical
potential V is given by the following equation.
V(x, y,
z) = 5x2 −
2xy + xyz
(a) Find the rate of change of the potential at P(4, 6,
4) in the direction of the vector v =
i + j − k.
(b) In which direction does V change most rapidly at
P?
(c) What is the maximum rate of change at P?

Suppose that over a certain region of space the electrical
potential V is given by the following equation. V(x,y,z)=3x^2 - 2xy
+xyz
a. find the rate of change of the potential at P (4,6,5) in the
direction of the vector v=i-j-k
b. In which direction does V change most rapidly at P?
c. What is the maximum rate of change at P?

The electric potential in a region of space is given by
V ( x,y,z ) = -x^2 + 2y^2 + 15. If a 5 Coulomb particle is placed
at position (x,y,z)=(-2,-2,0), what is the magnitude and direction
of the force it experiences?

The electric potential in a region of space as a function of
position x is given by the equation V(x) =
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2V/m2, β = 7V/m, and γ =
15V. All nonelectrical forces are negligible.
An electron starts at rest at x = 0 and travels to
x = 20 m.
Calculate the magnitude of the work done on the electron by the
electric field during this process.
Calculate the speed of the...

The potential in a region between x = 0 and x
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(a) Determine the potential at x = 0.
V
Determine the potential at x = 3.00 m.
V
Determine the potential at x = 6.00 m.
V
(b) Determine the magnitude and direction of the electric field at
x = 0.
magnitude
V/m
direction
---Select--- +x -x
Determine the magnitude...

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a) find the directional derivative of the potential at P(3,4,5)
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electric field at (x,y)=(2.0m,2.0m)? Give the direction as an angle
(in degrees) counterclockwise from the positive x-axis. THe
strenght of the electric field is 1200 V/m.

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