The electric potential in a region of space is V=350V?m/x2+y2?, where x and y ar

Question

The electric potential in a region of space is V=350V?m/x2+y2?, where x and y are in meters.

Part A: What is the strength of the electric field at (x,y)=(2.4m,1.8m)?

Part B: What is the direction of the electric field at (x,y)=(2.4m,1.8m)? Give the direction as an angle ccw from the positive x-axis.

Item 9 Part A The electric potential in a region of space is What is the strength of the electric field at (x, y) (2.4m, 1.8m)? Express your answer using two significant figures 350V.m, where z and y are in meters. Submit My Answers Give Up Part B What is the direction of the electric field at (x, y) = (2.4m, 1.8m)? Give the direction as an angle ccw from the positive x-axis Express your answer using two significant figures ccw from the positive z-axis Submit My Answers Give Up vid dback Continue

Explanation / Answer

A.For a potential of more than one variable, V (x, y), then

E (x, y) = -DV = - [dV/dx i + dV/dy j]

dV/dx = d[350/sqrt(x^2 + y^2)]/dx

you should know that

derivative of 1/(sqrt x) w.r.t. x is given by = -1/[2*(x)^(3/2)]

using this

dV/dx = -350*x/[(x^2 + y^2)^(3/2)]

dV/dy = -350*y/[(x^2 + y^2)^(3/2)]

E (x, y) = [350*x/[(x^2 + y^2)^(3/2)] + 350*y/[(x^2 + y^2)^(3/2)]]

E (x, y) = [350/(x^2 + y^2)^(3/2)]*(x i + y j)

at (2.4, 1.8)

E (2.4, 1.8)

E = [350/(2.4^2 + 1.8^2)^(3/2)]*(2.4 i + 1.8 j) = 12.96*(2.4 i + 1.8 j)

|E| = 12.96*sqrt(2.4^2 + 1.8^2) = 38.88 V/m

B.

directon

theta = arctan (Ey/Ex) = arctan (1.8/2.4)

theta = 36.87 deg

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