Question

The electric potential in an electric field is given by

V(x, y, z)= (-9.40 V/m5)x3y2 + (3.85 V/m4)y4 - (9.8 V/m2)zy.

Determine the unit vector form E = [ Ex V/m)i + (Ey V/m)j + (Ez V/m)k] of the electric field at the point whose coordinates are (-1.3 m, 2.3 m, 3.1 m). Give the x, y, z components of electric field in the form "+/-abc" V/m, or, "ab.c" V/m as is appropriate. For example, if you calculate the electric field as

E = -690 V/m i + 278 V/m j - 83.5 V/m k,

then your answer should be entered as

-690, +278, -83.5

Answer #1

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

A charge of 8x10-5 C is placed in an electric field
which components on x, y and z direction are given by Ex
= 3x103 N/C, Ey = -600 N/C and
Ez=0, respectively. What is the magnitude of the force
on the charged particle?
Lütfen birini seçin:
a. 62.5 N
b. 5 N
c. 0.25 N
d. 50 N
e. 0.5 N

Flowing through all space is an electric field E(x, y, z) =
αyz(x hat) + αxz(y hat) + αxy(z hat). Show that the curl of the
electric field vanishes, ∇ × E = 0. Use the definition of electric
potential to find the potential difference between the origin and r
= x(x hat) + y(y hat) + z(z hat), V (r) − V (0) = −(integral from 0
to r of (E · dl)). As the line integral is independent...

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).

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?

In the case of a uniform electric field and a flat surface, the
electric flux is defined as the dot product of the electric field
and the area, where the direction of the area is the normal to the
area pointing out of a closed region.
Consider a cube that measures 4.0 m on edge. The edges lie along
the coordinate axes x, y, and z, with one corner
at the origin, and the other corners having positive coordinates. A...

A uniform electric field is given (in units of N/C) by E = 63 i
– 87 j + 48 k , where i, j, k are unit vectors in the directions of
x, y, z axes respectively. Find the magnitude of the electric flux
through a circle of a 15 cm cm radius located in the xz-plane

1. Electric fields are E(x, y, z ;t) = Re [Es(x, y,
z)ejwt]
The magnetic field is H(x, y, z ;t) = Re [Hs(x, y,
z)ejwt].
Here, let's say Es and Hs are the pagers of electric and
magnetic fields.
(a) describe the Maxwell calculation using a pager.
(b) the medium is homogenous and the source free zone is
pager-based.
Describe Maxwell calculation.
(c) Using (b), electric field Es and magnetic field HS
Helmholtz calculation
Show satisfaction with ( k2...

A uniform electric field of magnitude 35 V/m is directed in the
negative y direction as shown in the figure. The coordinates of
point A are (-0.2, -0.3) m, and those of point B are (0.4, 0.5) m.
The electric potential difference VB - VA using the dashed-line
path.

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.

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