The electric potential is given in a region by V = 5000 x^2 + 2000 y^3 x (the co

Question

The electric potential is given in a region by V = 5000 x^2 + 2000 y^3 x (the constants with units are 5000 V/m^2 and 2000 V/m^4). Find the electric field components as functions of x and y. Find the electric field components at x = 5 m, y = 7 m. What is the change in potential energy for a 5 mu C charged particle with a mass of 0.5 g as it moves from x = 0, y = 0 to x = 5m, y = 7 m? If the speed of the particle as it passes x = 0, y = 0 is 300 m/s. what is the speed of the panicle as it passes x = 5 m, y = 7 m?

Explanation / Answer

  Take partial derivatives with respect to each coordinate:
V = 5000x^2 + 2000y^3x
Ex = -V/x = -[5000*(2x) + 2000y^3] = -10000x - 2000y^3
Ey = -V/y = -[2000(3y^2x)] = -6000y^2x

At x = 5 and y = 7

Ex = -[10000 x 5 + 2000 x 343]

Ex = 7.36 x 10^5 V/m

Ey = - 6000 x 49 x 5

Ey = 1.47 x 10^6 V/m

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