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1) Given: V = αx2y2 + βz2(x2 - γ) + δy3z
Where α = 5 V/m4, β = 6.6 V/m4, γ = 3.4 m2, and δ = 5.3 V/m4.
What is the y component of the electric field Ey at (4.6m, -4 m, 4.7 m)? Answer in units of V/m.

2) The electric potential in a certain region is:
V = ax2 + bx + c,
Where a = 10 V/m2, b = -19 V/m, and c = 55 V.
Determine the electric field at x = 3 m. Answer in units of V/m.

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With complete formulas and calculations, the problems are answered.

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1.)
Electric field in y direction:
Ey = -(dp(V)/dy).j
where, dp(V)/dy = partial derivative of V with respect to y.
because,
V = Ax^2y^2 + Bz^2(x^2-G) + DY^3z
where,
A==alpha = 5 unit, ...

Solution provided by:
Amrit Lal Ahuja, PhD (IP)
Education
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
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