1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
topjm [15]
3 years ago
11

The electric potential in a certain region is given by the equation V(x,y,z) = 3αx2y3 - 2γx2y4z2 where the potential is in volts

when the positions are given in meters. The constants in this equation are α = 2.5 V/m5 and γ = 1.33 V/m8
(a) Write an equation for the x-component of the electric field.

(b) Write an equation for the y-component of the electric field.

(c) Write an equation for the z-component of the electric field.

(d) Calculate the magnitude of the electric field at the point x13-(-5.0, 2.0, 1.5) m in units of newtons per coulomb.
Physics
1 answer:
Mila [183]3 years ago
7 0

Answer:

a) An equation for the x-component of the electric field.

Eₓ = (-15xy³ + 5.32xy⁴z²) N/C

b) An equation for the y-component of the electric field.

Eᵧ = (-22.5x²y² + 10.64x²y³z²) N/C

c) An equation for the z-component of the electric field.

Ez = (5.32x²y⁴z) N/C

d) At (-5.0, 2.0, 1.5) m, the electric field is given as

E = (-357.6î + 2,538ĵ + 3,192ķ) N/C

Magnitude of the electric field = 4,093.7 N/C

Explanation:

The electric field is given by the negative of the gradient of the electric potential,

E = −grad V

E = - ∇V

The electric potential is given as

V(x,y,z) = 3αx²y³ - 2γx²y⁴z²

α = 2.5 V/m⁵ and γ = 1.33 V/m⁸

V(x,y,z) = 7.5x²y³ - 2.66x²y⁴z²

grad = ∇ = (∂/∂x)î + (∂/∂y)ĵ + (∂/∂z)ķ

E = -grad V = -∇V

= -[(∂V/∂x)î + (∂V/∂y)ĵ + (∂V/∂z)ķ

E = -(∂V/∂x)î - (∂V/∂y)ĵ - (∂V/∂z)ķ

E = Eₓî + Eᵧĵ + Ez ķ

a) An equation for the x-component of the electric field.

Eₓ = -(∂V/∂x) = -(∂/∂x)(V)

= -(∂/∂x)(7.5x²y³ - 2.66x²y⁴z²)

= -(15xy³ - 5.32xy⁴z²)

= (-15xy³ + 5.32xy⁴z²)

b) An equation for the y-component of the electric field.

Eᵧ = -(∂V/∂y) = -(∂/∂x)(V)

= -(∂/∂y)(7.5x²y³ - 2.66x²y⁴z²)

= -(22.5x²y² - 10.64x²y³z²)

= (-22.5x²y² + 10.64x²y³z²)

c) An equation for the z-component of the electric field.

Ez = -(∂V/∂z) = -(∂/∂x)(V)

= -(∂/∂z)(7.5x²y³ - 2.66x²y⁴z²)

= -(0 - 5.32x²y⁴z)

= (5.32x²y⁴z)

d) E = Eₓî + Eᵧĵ + Ez ķ

E = (-15xy³ + 5.32xy⁴z²)î + (-22.5x²y² + 10.64x²y³z²)ĵ + (5.32x²y⁴z) ķ

At (-5.0, 2.0, 1.5) m

x = -5 m

y = 2 m

z = 1.5 m

Eₓ = (-15xy³ + 5.32xy⁴z²)

= (-15×-5×2³) + (5.32×-5×2⁴×1.5²)

= 600 - 957.6 = -357.6

Eᵧ = (-22.5x²y² + 10.64x²y³z²)

= (-22.5×(-5)²×2²) + (10.64×(-5)²×2³×1.5²)

= -2250 + 4788 = 2538

Ez = (5.32x²y⁴z) = (5.32×(-5)²×2⁴×1.5)

= 3192

E = -357.6î + 2,538ĵ + 3,192ķ

Magnitude = /E/ = √[(-357.6)² + 2538² + 3192²]

= 4,093.6763135353 = 4,093.7 N/C

Hope this Helps!!!!

You might be interested in
Which best describes a difference between laser light and regular light?
Inga [223]
The basic difference is that the ordinary sources are incoherent that means that the discrete frequencies merge up to give an intermediate between the maximum and minimum frequencies. While the laser is coherent containing the single frequency with maximum amplitude. thus travelling far.
4 0
3 years ago
Most of the Earth's volcanoes occur
timofeeve [1]

Answer:

A.

Explanation:

NEAR THE CENTER OF TECTONIC PLATES.

3 0
3 years ago
Brandon buys a new Seadoo. He goes 22 km north from the beach. He then goes 11km to the east. Then chases a boat 3 km north. Wha
KIM [24]

Answer:

36kms

Explanation:

22+1=33

33+3=36

6 0
3 years ago
A 4.0kg block is sliding with a constant velocity of 3.0m/s on a frictionless table that is 0.5m high. If all of the block’s ene
MArishka [77]

Answer:

Velocity = 4.33[m/s]

Explanation:

The total energy or mechanical energy is the sum of the potential energy plus the kinetic energy, as it is known the velocity and the height, we can determine the total energy.

E_{M}=E_{p}  + E_{k} \\E_{p} = potential energy [J]\\E_{k} = kinetic energy [J]\\where:\\E_{p} =m*g*h\\E_{p} = 4*9.81*0.5=19.62[J]\\E_{k}=\frac{1}{2} *m*v^{2}  \\E_{k}=\frac{1}{2} *4*(3)^{2} \\E_{k}=18[J]\\Therefore\\E_{M} =18+19.62\\E_{M}=37.62[J]

All this energy will become kinetic energy and we can find the velocity.

37.62=\frac{1}{2} *m*v^{2} \\v=\sqrt{\frac{37.62*2}{4} } \\v=4.33[m/s]

8 0
3 years ago
How much work is required to stop an electron (m = 9.11 \times 10^ - 31 kg) which is moving with a speed of 2.10
Karo-lina-s [1.5K]

Answer:

-2.00876\times 10^{-18}\ J

Explanation:

v = Speed of electron = 2.1\times 10^6\ m/s (generally the order of magnitude is 6)

m = Mass of electron = 9.11\times 10^{-31}\ kg

Work done would be done by

W=K_i-K_f\\\Rightarrow W=0-\dfrac{1}{2}mv^2\\\Rightarrow W=0-\dfrac{1}{2}\times 9.11\times 10^{-31}\times (2.1\times 10^6)^2\\\Rightarrow W=-2.00876\times 10^{-18}\ J

The work required to stop the electron is -2.00876\times 10^{-18}\ J

6 0
3 years ago
Other questions:
  • A 2.0 kg mass weighs 10 Newtons on planet X. what is the acceleration due to gravity on planet X? Show the work.
    8·1 answer
  • What did scientists predict the big bang should have left?
    12·2 answers
  • I need these ASAP 20 POINTS!!
    15·1 answer
  • Which is NOT a subatomic particle
    12·1 answer
  • Which part of an atom is actively exchanged or shared in a chemical bond?
    11·2 answers
  • Where is the antinode of a standing wave?
    10·1 answer
  • A circuit maintains a constant resistance. If the current in the circuit is doubled, what is the effect on the power dissipated
    12·1 answer
  • A rectangular certificate has a perimeter of 32 inches. Its area is 63 square inches. What are the dimensions of the certificate
    8·1 answer
  • A frog has a pulmocutaneous artery and vein which compares to the human pulmonary artery and vein. What two organs do these bloo
    11·1 answer
  • Which mineral is also an element graphite courts calcite hematite
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!