Calculate $\operatorname { curl } \overline { \bar { H } }$ where $ { \vec{ H } } = 9 x \vec { i } - 8 x y \vec { j } + x z ^ { 5 } \vec { k }$
A) $\operatorname { cur } 1 { \vec { H } } = z ^ { 5 } \vec { j } - 8 y \vec { k }$
B) $\operatorname { curl } { \vec { H } } = - z ^ { 5 } \vec { j } - 8 y \vec { k }$
C) $\operatorname { curl } { \vec{ H } } = z ^ { 5 } \vec { i } - 8 y \vec { k }$
D) $\operatorname { curl } { \vec { H } } = - z ^ { 5 } \vec { j } + 8 y \vec { k }$

Question

Calculate $\operatorname { curl } \overline { \bar { H } }$ where $ { \vec{ H } } = 9 x \vec { i } - 8 x y \vec { j } + x z ^ { 5 } \vec { k }$
A) $\operatorname { cur } 1  { \vec { H } } = z ^ { 5 } \vec { j } - 8 y \vec { k }$
B) $\operatorname { curl } { \vec { H } } = - z ^ { 5 } \vec { j } - 8 y \vec { k }$
C) $\operatorname { curl }  { \vec{ H } } = z ^ { 5 } \vec { i } - 8 y \vec { k }$
D) $\operatorname { curl }   { \vec { H } } = - z ^ { 5 } \vec { j } + 8 y \vec { k }$

Quizplus · Accepted Answer

The curl of a vector field $\vec{H} = 9x\vec{i} - 8xy\vec{j} + xz^5\vec{k}$ is calculated using the determinant of a matrix that includes the unit vectors $\vec{i}, \vec{j}, \vec{k}$, the partial derivatives with respect to $x, y, z$ in the middle row, and the components of $\vec{H}$ in the bottom row. The calculation yields $-z^5\vec{j} - 8y\vec{k}$, making option B correct.

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Calculate $\operatorname { curl } \overline { \bar { H } }$