Question
PLEASE HELP! !
In a square 2m × 2m region of space the electric potential, V(x, y, z), is well described by the function V (x, y, z)=Ax^2y+By. A and B are constants with A=2.0 V/m^3 and B=3.0 V/m. The diagram below shows a contour plot of V (x, y, z) in the x-y plane.
Physies 151 Name In a square 2mx2m region of space the electric potential, P(x, y,z), is well described by the function v,ya)-Axy+By. A and B and are constants with A 20V/m and 8-3.0V/m. The diagram below shows a contour plot of V(x, y, z) in the x-y plane. 13 The curves (contours) in the diagram are lines of constant potential. In other words, every point on a given line is at the same potential. The contours shown have been chosen so that the potential difference between adjacent lines is 1.0 V. The potential at the origin (0 m, 0 m) is 0 V. Therefore, since only differences in potential mater, the value of the potential at any other point is with respect to the potential at the origin. A. Using (x,y,)-Ay+ By caleulate the potential at point P which is at x- 1.0 m,y-1.5 m. By doing so you will have determined the value of the equipotential line on which point P sits. Show your calculation for credit Using V(r,y,z)=Ax2y+ By calculate the x andy coordinates orat least four points in the region shown that are at a potential of 8.5 V. Show your calculations for credit. carefully mark the four points on the diagram B. After completing the calculations C. In symbolic mathematical notation write down the relationship between the electric field E(x, y,:) and the electric potential Vx.y,:). This can be written in two forms. One form tells you how to calculate r, y) if E, y.z) is known. The other form tells you how to calculate E,y,if vx,y.a) is known. The latter is what we want, because in this problem V(x. y,z) is known, and soon you will have to calculate Ex,y,:). Your equation must be a vector equation, starting Ex.y.:)- D. By performing partial derivatives of Vi,J,z) obtain symbolic expressions for the x and y components of the electric field at any point. (The : component is zero and will be ignored.) Show your work. E. Ifan electron was placed at rest at point P and released it would accelerate because there would be an electric force acting on it. Calculate the initial acceleration of the electron in polar form. Show all calculations for credit. F. Attach the tails of four arrows to point P to represent the following four quantities: i) an arrow representing of the electron's initial acceleration, ii) an arrow representing the y-component of the the x-component electron's initinl acceleration, iii) an arrow representing the resultant acceleration, and iv) an arrow representing the electric field at point P
Explanation / Answer
(A) We have equation for potential V(x, y, z) = (A =2)x2y +(B=3)y
So at the point (1, 1.5) V(x,y,z)= 7.5 Volt
(B) Now we have
2x2y+3y= 8.5
for finding four different value we will put either for x or y and find for other variable.
For ex. At x=0, y will be y=2.833
At x=1 , y=1.7
at x=2 , y=.7727
at x=3 y = .404
(C) To find electric field from potential
(D)Ex = 4xy, Ey = (3+2x2)
(E) Electrostatic force = Electric field*q (charge on electron) = (mass of electron)*acceleration
