Potential and solenoidal fields/Potential and solenoidal…

MathProblemsBank banner

MathProblemsBank banner

Math Problems and solutions

Problem list Free problems

Attention! If a subsection is selected, then the search will be performed in it!

(3) Problem: Show that the vector field \( \vec{a} \) is potential and find its potential: \[ \begin{array}{l} \vec{a}=y z \cos x y \cdot \vec{\imath}+z x \cos x y \cdot \vec{\jmath}+\sin x y \cdot \vec{k}, \\ M_{1}(1,1,1), \quad M_{2}(0,0,0) \end{array} \]

9.9.1 Potential and solenoidal fields

3.06 $

3) Problem: Show that the field \( \vec{a} \) is potential and find its potential: \[ \vec{a}=\left(\frac{y}{z}+2 x\right) \vec{\imath}+\frac{x}{z} \vec{\jmath}-\frac{x y}{z^{2}} \vec{k} . \]

9.9.2 Potential and solenoidal fields

1.02 $

Problem: Show that the field \( \vec{a} \) is potential and find its potential: \[ \vec{a}=\left(\frac{y}{z}+z\right) \vec{\imath}+\left(\frac{x}{z}-\frac{1}{y^{2}}\right) \vec{\jmath}+\left(x-\frac{x y}{z^{2}}\right) \vec{k} . \]

9.9.3 Potential and solenoidal fields

1.27 $

Problem: Is the vector field \( \vec{a}=x z^{2} \vec{\imath}+(y-1) \vec{\jmath}+x^{2} z \vec{k} \) : a) potential. If yes, find its potential, b) solenoidal?

9.9.4 Potential and solenoidal fields

3.82 $