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The Expert TAIHuman- x C Chegg study IGuided Sc x C Chegg Study Questions x Secure h ps://usq45tx heexpertta.co /Take Tu alAssignment..aspx (s%) Problem 5: The electric potential in a certain region is given by the equation VorJ, 3ax2,3 -2:m2,4:2 where the potential is in volts when the positions are given in meters The constants in this equation are given below. Randomized Variables a 3 4.7 VIm Assignment Status Click here for Go 25% Part (a) Write an equation for the x-component of the electric field. detailed view Grade Summary Deduct Problem Status Late Work 7500 Late Potential 70.5% i Completed Completed Submissions Part Attempts remaining: S 4 Partial per attempt detailed view 5 Partial Completed Completed Partial Feedback 0% deduction per feedback. Hints 3 for a 0% deduction Hints remaining .0 9 Completed How is the electric field related to the potential? 10 Completed Do not forget the negative Bign 11 Part -Treaty and as constantEwhen you tal:e the derivative with respect 12 Partial to X. 13 Completed 25% Part (c) Write an equation for the z-component of the electric field 25% Part (d calculate the magnitude of the electric field at the point (my :D (5.0. 2.0. 1.5 m in units of newtons per coulomb Ask me anything 5.23 PM

Explanation / Answer

Given

potential equation V(x,y,z) = 3ax^2 y^3 - 2gx^2y^4z^2

and a = 4.7 V/m^5
g = 1.34 V/m^8

we know that E(x) = -dV/dx

here the derivative is partial differentiation

   E(x) = -d(3ax^2 y^3 - 2gx^2y^4z^2)/dx = -3a(2x)y^3 +2g(2x)y^4z^2

   E(y) = -d(3ax^2 y^3 - 2gx^2y^4z^2)/dy = -3ax^2(3y^2)+2g 2x^2(4y^3)z^2

   E(z) =-d(3ax^2 y^3 - 2gx^2y^4z^2)/dz = - 0 +2g x^2(y^4)(2z)

now the magnitude of the electricfield at (x1,y1,z1) = (-5 ,2,1.5) is

   E = E(x)+E(y)+E(z)
   E = ( -3a(2x)y^3 +2g(2x)y^4z^2)i +(-3ax^2(3y^2)+2g 2x^2(4y^3)z^2)j +(2g x^2(y^4)(2z))

substituting the values of x,y,z and a,g
2
   E = (-3*4.7*(2(-5)(1.5)^3+2*1.34(2(-5)(2)^4(1.5)^2)) i + (-3*4.7(-5)^2*3*2^2+2*1.34*2(-5)^2*4(2)^3(1.5)^2)j+ (2*1.34*(-5)^2*2^4*2*1.5)k

   magnitude is E = sqrt(Ex^2+Ey^2+Ez^2)

       E = sqrt((14079.555)^2+(5418)^2+(3216)^2) N/C

       E = 15425.0202 N/C

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