Five Hundred eight thousand, nine hundred one

In a certain region of space, the potential is given by v=2x−5x2y 3yz2. How much is the magnitude of the electric field at point

Masja [62]

The magnitude of the electric field at the point (-2, 2, 0) is 46.52 V/m

<h3>How to calculate the electric field?</h3>

Since in a certain region of space, the potential is given by v = 2x − 5x²y 3yz²,

The electric field, E = -grad(V) where grad(V) = (dV/dx)i + (dV/dy)j + (dV/dz)k

Since V = 2x − 5x²y + 3yz²

dV/dx = d(2x − 5x²y + 3yz²)/dx

= d2x/dx - d5x²y/dx + d3yz²/dx

= 2 - 10xy + 0

= 2 - 10xy

dV/dy = d(2x − 5x²y + 3yz²)/dy

= d2x/dy - d5x²y/dy + d3yz²/dy

= 0 - 5x² + 3z²

= - 5x² + 3z²

dV/dz = d(2x − 5x²y + 3yz²)/dz

= d2x/dz - d5x²y/dz + d3yz²/dz

= 0 - 0 + 6z

= 6z

<h3>The electric field</h3>

So, E = -grad(V)

= -[(dV/dx)i + (dV/dy)j + (dV/dz)k]

= -[(2 - 10xy)i + (- 5x² + 3z²)j + (6z)k]

So, the electric field at (-2, 2, 0) is

E = -[(2 - 10xy)i + (- 5x² + 3z²)j + (6z)k]

E = -[(2 - 10(-2)(2))i + (- 5(2)² + 3(0)²)j + (6(0))k]

E = -[(2 + 40)i + (- 5(4) + 0)j + (0)k]

E = -[42i + (-20 + 0)j + (0)k]

E = -[42i - 20j + 0k]

E = -42i + 20j - 0k

<h3>The magnitude of the electric field</h3>

So, the magnitude of E at (-2, 2, 0) is

|E| = √[(-42)² + 20² + 0²]

= √[1764 + 400 + 0]

= √2164

= 46.52 V/m

So, the magnitude of the electric field at the point (-2, 2, 0) is 46.52 V/m

Learn more about electric field here:

brainly.com/question/25751825

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3 0

2 years ago

What do you do to the b value to correctly complete the square?

mash [69]

Answer:

Step-by-step explanation:

B is correct: We Divide it (the coefficient b) by 2 and square the result.

3 0

2 years ago

Read 2 more answers

Identify the errors made in the finding the inverse of y= x^2 +12x

alex41 [277]

9514 1404 393

Answer:

y was not substituted for every x

Step-by-step explanation:

To find the inverse of ...

y = f(x)

you need to solve ...

x = f(y)

Here, f(x) = x^2 +12x, so f(y) = y^2 +12y

This is not the expression we see on the right of ...

x = y^2 +12x

Apparently y was not properly substituted into f(x).

5 0

3 years ago

A jogger running around a rectangular park takes a shortcut back to her car by jogging from one corner of the park to the diagon

coldgirl [10]

Answer:the short cut is 55 meters.

Step-by-step explanation:

The park around which the jogger jogged is rectangular in shape. The Short cut that the jogger jogged through to her car is the diagonal of the rectangle. The diagonal becomes the hypotenuse of the rectangle. The sides of the field becomes the opposite side and adjacent side of the triangle. To determine the length of the diagonal, we would apply Pythagoras theorem. It is expressed as

Hypotenuse^2 = opposite side^2 + adjacent side^2

Hypotenuse^2 = 44^2 + 33^2 = 3025

Hypotenuse = √3025

Hypotenuse = 55 meters

8 0

3 years ago

You are remodeling your bedroom. You will paint all 4 walls and the door. There are no windows in the room. The floor is 9' by 1

Aleksandr [31]

Answer:

Part 1) The area of the 4 walls is $368\ ft^2$

Part 2) You will have to buy 2 gallons

Part 3) You will have to buy 3 gallons

Part 4) $\$75$

Part 5) The area of the floor is $126\ ft^2$

Part 6) $\$850.5$

Part 7) $\$1,008$

Part 8) $\$472.5$

Step-by-step explanation:

Part 1) What is the area of all 4 walls together?

we know that

The area of all 4 walls together is equal to the perimeter of the floor multiplied by the height of the wall (8 ft)

so

The perimeter of the floor is

$P=2(9+14)=46\ ft$

The area of the walls is

$46(8)=368\ ft^2$

Part 2) If a gallon of paint covers 350 sq. ft., How many gallons will you have to buy?

using proportion

$\frac{1}{350}\ \frac{gal}{ft^2}=\frac{x}{368}\ \frac{gal}{ft^2}\\\\x=368/350\\\\x=1.05\ gal$

Remember that you can't buy a fraction of gallon

so

You will have to buy 2 gallons

Part 3) How many gallons will it take to put on 2 coats of paint?

Now the area will be

$368(2)=736\ ft^2$

using proportion

$\frac{1}{350}\ \frac{gal}{ft^2}=\frac{x}{736}\ \frac{gal}{ft^2}\\\\x=736/350\\\\x=2.10\ gal$

Remember that you can't buy a fraction of gallon

so

You will have to buy 3 gallons

Part 4) If the paint costs $25 per gallon, and you are applying 2 coats of paint, how much will you spend on paint?

To find the cost multiply the number of gallons by $25 per gallon

so

$3(25)=\$75$

Part 5) What is the area of the floor?

The area of the floor (rectangle ) is equal to multiply the length of the floor by the width of the floor

$A=(9)(14)=126\ ft^2$

Part 6) What is the cost to redo the floor in oak?

To find the cost multiply the area of the floor by $6.75 per square foot

so

$126(6.75)=\$850.5$

Part 7) What is the cost to redo the floor in maple?

To find the cost multiply the area of the floor by $8.00 per square foot

so

$126(8.00)=\$1,008$

Part 8) What is the cost to redo the floor in carpet?

To find the cost multiply the area of the floor by $3.75 per square foot

so

$126(3.75)=\$472.5$

5 0

3 years ago