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(D) The loop $ABCDEFA$ consists of two planar surfaces: the rectangle $ABCD$ in the $xy$-plane and the rectangle $ADEF$ in the $yz$-plane.The area vec

Vedclass · Accepted Answer

$175$

Vedclass · Answer

(D) The loop $ABCDEFA$ consists of two planar surfaces: the rectangle $ABCD$ in the $xy$-plane and the rectangle $ADEF$ in the $yz$-plane.The area vector for the rectangle $ABCD$ (in the $xy$-plane) is $\overrightarrow{A}_{ABCD} = (5 	imes 5) \hat{k} = 25 \hat{k} \; 	ext{m}^2$.The area vector for the rectangle $ADEF$ (in the $yz$-plane) is $\overrightarrow{A}_{ADEF} = (5 	imes 5) \hat{i} = 25 \hat{i} \; 	ext{m}^2$.The net area vector is $\overrightarrow{A}_{net} = \overrightarrow{A}_{ABCD} + \overrightarrow{A}_{ADEF} = 25 \hat{i} + 25 \hat{k} \; 	ext{m}^2$.The magnetic field is given as $\overrightarrow{B} = 3 \hat{i} + 4 \hat{k} \; 	ext{T}$.The magnetic flux $\phi$ is calculated using the dot product: $\phi = \overrightarrow{B} \cdot \overrightarrow{A}_{net}$.$\phi = (3 \hat{i} + 4 \hat{k}) \cdot (25 \hat{i} + 25 \hat{k})$$\phi = (3 	imes 25) + (4 	imes 25) = 75 + 100 = 175 \; 	ext{Wb}$.Thus,the magnetic flux through the loop is $175 \; 	ext{Wb}$.

$A$ loop $ABCDEFA$ of straight edges has six corner points $A(0,0,0), B(5,0,0), C(5,5,0), D(0,5,0), E(0,5,5)$ and $F(0,0,5)$. The magnetic field in this region is $\overrightarrow{B}=(3 \hat{i}+4 \hat{k}) \; T$. The quantity of magnetic flux through the loop $ABCDEFA$ (in $\text{Wb}$) is:

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