Question

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.

Answer #1

The electric potential in a region of space is V=( 260 x2− 160
y2)V, where x and y are in meters. What is the direction of the
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.

The electric potential in a region of space is V=( 260 x2− 160
y2)V, where x and y are in meters. What is the strength of the
electric field at (x,y)=(2.0m,2.0m)
?
What is the direction of the electric field
at (x,y)=(2.0m,2.0m)? Give the
direction as an angle (in degrees) counterclockwise from the
positive x-axis.

The electric potential (V) at a certain point in space is given
by: V(x, y, z) = 5x2-3xy+xyz
a) find the directional derivative of the potential at P(3,4,5)
in the direction of the vector v=i+j+k
b) calculate the gradient of the electric potential

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) =
αx2 + βx - γ, where α =
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
= 6.00 m is V = a + bx, where a
= 19.4 V and b = -6.70 V/m.
(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...

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 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).

In a region of space, there is an electric field. At a
particular point, the electric field is E = (5.0(i-hat) +
12(j-hat)) V/m. A point charge of −300 nC is placed at this
point.
What is the magnitude of the force on the point charge?
What is the x-component and y-component of the force on the
point charge?
What is the direction of the force on the point charge?

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