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
PSYCHO15rus [73]
3 years ago
14

The electric field in the​ xy-plane due to an infinite line of charge along the​ z-axis is a gradient field with a potential fun

ction
​V(x,y)equals=c ln (ro/√ x²+y²)

where c > 0 is a constant and r0 is a reference distance at which the potential is assumed to be 0.

Required:
Find the components of the electric field in the​ x- and​ y-directions, where E​(x,y) =∇V (x,y )
Mathematics
1 answer:
Olenka [21]3 years ago
3 0

Answer:

c(x,y)/(x²+y²)

Step-by-step explanation:

Since E​(x,y) = -∇V (x,y ) and V(x,y) =c ln (ro/√ x²+y²)

Let ro/√(x²+y²) = u and √(x²+y²) = v

dV/du = c/u = c√(x²+y²)/ro,

du/dv =  -ro/(x²+y²) = -ro/² and dv/dx = x/√(x²+y²)

Using the chain rule,

So dV/dx = dV/du × du/dv × dv/dx

= c√(x²+y²)/ro × -ro/(x²+y²) × x/√(x²+y²)

dV/dx = -cx/(x²+y²)

- dV/dx = -(-cx/(x²+y²)) = cx/(x²+y²)

Also, dv/dy = y/√(x²+y²)

Using the chain rule

dV/dy = dV/du × du/dv × dv/dy

= c√(x²+y²)/ro × -ro/(x²+y²) × y/√(x²+y²)

dV/dy = -cy/(x²+y²)

- dV/dy = -(-cy/(x²+y²)) = cy/(x²+y²)

E(x,y) = -∇V (x,y )

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

= [cx/(x²+y²)]i +[ cy/(x²+y²)]j

= c(x,y)/(x²+y²)

You might be interested in
A principal of 5500 is invested in an account paying the amount of an annual rate of 5%. Find the amount in the account after 4
kondor19780726 [428]

Answer:

bnjkkkkkkkkkklllkkll

7 0
3 years ago
A line is perpendicular to<br> y = - 1/4x-9<br> What is the slope of this<br> perpendicular line?
Kryger [21]

Answer:

A line is perpendicular to

y = - 1/4x-9

comparing with y = MX+ c

m=-1/4.

slope =-1/4

7 0
3 years ago
I NEED HELP! ASAP, THIS IS SO HARD AND MY BRAIN HURTS, IF U HELP ME WITH OTHER QUESTIONS LIKE THIS ILL GIVE U 50+ POINTS
Dimas [21]

Answer:

24.3

Step-by-step explanation:

We need to follow the order of operations PEMDAS:

  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

Carry out the operation in the parentheses first:

   3³ + 14.7 ÷ 7 - (1.2 × 4)

⇒ 3³ + 14.7 ÷ 7 - 4.8

Now the exponent:

⇒ 3³ + 14.7 ÷ 7 - 4.8

⇒ (3 × 3 × 3) + 14.7 ÷ 7 - 4.8

⇒ 27 + 14.7 ÷ 7 - 4.8

Now, the division (there is no multiplication):

⇒ 27 + 14.7 ÷ 7 - 4.8

⇒ 27 + 2.1 - 4.8

Finally, carry out the addition and subtraction (from left to right)

⇒ 27 + 2.1 - 4.8

⇒ 29.1 - 4.8

⇒ 24.3

8 0
2 years ago
The rule T 5, -0.5° Ro, 1800(x, ) is applied to FGH to
Yuki888 [10]

Answer:

Step-by-step explanation:

Given rule for the multiple translations is,

T_{5,-0.5}.R_{0.180^{\circ}}(x,y)

Apply the rule R_{0,180^{\circ}} first.

(x, y) → (-x, -y)

This rule illustrates a rotation of the triangle FGH by 180° about the origin,

Vertices of ΔFGH are,

F → (1, 1)

G → (4, 5)

H → (5, 1)

After rotation vertices of the image triangle are,

F' → (-1, -1)

G' → (-4, -5)

H' → (-5, -1)

Further apply the rule,

T_{5,-0.5}

(x, y) → (x + 5, y - 0.5)

By this rule of translation,

F'(-1, -1) → F"{(-1 + 5), (-1 - 0.5)}

            → F"(4, -1.5)

G'(-4, -5) → G"[(-4 + 5), (-5 - 0.5)]

              → G"(1, -5.5)

H'(-5, -1) → H"[(-5 + 5), (-1 -0.5)]

             → H"(0, -1.5)

8 0
2 years ago
HALP MA PLS!!!!!!!!!!!!!!!!!!!!!!
Inessa05 [86]

Answer:

48 dollars.

Step-by-step explanation:

If you look up "40 percent off of 85" you'll get 48.

5 0
3 years ago
Read 2 more answers
Other questions:
  • Rewrite as a simplified fraction<br> 2.267 = ?
    10·2 answers
  • What is the value of the expression (8-3) times 2+(5 times6) -5*5
    15·2 answers
  • An investment of 75,000 increases at a rate 12.5% per year. Find the value of the investment after 30 years.
    15·2 answers
  • How many possible combinations are there on a 4 digit lock using numbers 0-9, if duplicate numbers are not allowed?
    7·1 answer
  • classify the triangle by its angles and its sides. explain how you knew which classifications to use
    8·1 answer
  • Y + 2 = -3 (x - 4) Complete the missing value in the solution to the equation. (____, -2)
    5·2 answers
  • B(x)=x^3+x^2-9x-9 immmmm loooooost helpppppp
    8·2 answers
  • What is the probability that a randomly selected number from 30 to 61 is divisible by 7 and then divisible by 20 after replacing
    8·1 answer
  • Pleas help due to night​​
    9·2 answers
  • A coffee shop sells their coffee beans by the pound. the table below shows the cost in dollars for a pound of two different type
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!