Question

The electric potential (V) at a certain point in space is given by: V(x, y, z)...

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

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose that over a certain region of space the electrical potential V is given by the...
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...
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?
1-Find equations of the following. 2(x − 9)2 + (y − 1)2 + (z − 8)2...
1-Find equations of the following. 2(x − 9)2 + (y − 1)2 + (z − 8)2 = 10,    (10, 3, 10) (a) the tangent plane ----------------------------------------------------------------------------------------------------------------------------------------------------------- 2-Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 4x2 − 3xy + xyz (a) Find the rate of change of the potential at P(3, 2, 5) in the direction of the vector v = i + j − k. (b) In...
The electric potential in an electric field is given by V(x, y, z)= (-9.40 V/m5)x3y2 +...
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...
Find directional derivative of the function f(x, y, z) = 5x2 + 2xy – 3y2z at...
Find directional derivative of the function f(x, y, z) = 5x2 + 2xy – 3y2z at P(1, 0, 1) in the direction v = i + j – k .
The electric potential in a region of space is given by V ( x,y,z ) =...
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 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...
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.
. For the function f(x, y) = xye^x−y , at the point (2, 2) (a) find...
. For the function f(x, y) = xye^x−y , at the point (2, 2) (a) find the gradient. (b) find the directional derivative in the direction of the vector 3i − j. (c) in the direction of which unit vector is the rate of increase maximum? What is the maximum rate of increase? (d) in the direction of which unit vector(s) is the directional derivative zero?
The electric potential in a region is given by V(x,y,z) = -10.0x2 + 20.0xyz + 6.0y3...
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 function f(x; y) = xye^x-y, at the point (2; 2) (1)find the gradient. (2) find...
the function f(x; y) = xye^x-y, at the point (2; 2) (1)find the gradient. (2) find the directional derivative in the direction of the vector 3i - j. (3)find the direction of which unit vector is the rate of increase maximum? What is the maxi- mum rate of increase? (4)find the direction of which unit vector(s) is the directional derivative zero?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT