### Problem Statement:(a) **Electric Potential Equation:**The electric potential in a region is given by the equation:\[ V(x, y) = (2.00 \times 10^5 \, \frac{V}{m^5}) x^3 yz + (3.00 \times 10^5 \, \frac{V}{m^3}) x^3 + (1.00 \times 10^5 \, \frac{V}{m^2}) z^2 \]**Question:**What is the electric field at position \( (30 \text{cm}, -10 \text{cm}, 10 \text{cm}) \)? Provide your answer in vector component notation.(b) **Magnetic Field Calculation:**A point charge of value \( q = 1.10 \, \mu C \) has a speed of \( \vec{v} = -3.23 \times 10^4 \, \frac{m}{s} \, \hat{j} - 1.31 \times 10^4 \, \frac{m}{s} \, \hat{k} \) when it is at the point \( (0.00 \, cm, 0.00 \, cm, 0.00 \, cm) \).**Question:**What is the magnetic field vector in component form at position \( (30 \text{cm}, -10 \text{cm}, 10 \text{cm}) \)?(c) **Net Force Calculation:**If a region exists with the potential from part (a) and the charge from part (b), what is the net force on a \( 65.0 \, mC \) charge at point \( (30 \text{cm}, -10 \text{cm}, 10 \text{cm}) \) moving at speed \( \vec{v} = 2.20 \times 10^6 \, \frac{m}{s} \, \hat{i} + 1.30 \times 10^6 \, \frac{m}{s} \, \hat{j} \) ?Graphical or diagrammatic elements are not present in this section, so the problem description is purely textual with an emphasis on mathematical expressions and physics principles.

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Answered: (a) The electric potential in a region…

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