A uniform electric field E→ exists in a region of space. Three squares having areas 2 m2, 3 m2 and 4 m2 lie in xy, yz and zx planes respectively. If the electric flux through the areas are 4 V-m, 9 V-m and 8 V-m respectively, then the electric field may be

Let the electric field be E→=Exi^+Eyj^+Ezk^Given Axy→ =2k^m2, Ayz→ =3i^m2 and Azx→ =4j^m2,Φxy= E→Axy→ ==Ez.Axy⇒Ez=42V/m=2V/mΦyz= E→Ayz→ ==Ex.Ayz⇒Ex=93V/m=3V/mΦzx= E→Azx→ ==EyAzx⇒Ey=84V−m=2V−m∴E→=3i^+2j^+2k^V/m

A uniform electric field E→ exists in a region of space. Three squares having areas 2 m2, 3 m2 and 4 m2 lie in xy, yz and zx planes respectively. If the electric flux through the areas are 4 V-m, 9 V-m and 8 V-m respectively, then the electric field may be

Let the electric field be E→=Exi^+Eyj^+Ezk^Given Axy→ =2k^m2, Ayz→ =3i^m2 and Azx→ =4j^m2,Φxy= E→Axy→ ==Ez.Axy⇒Ez=42V/m=2V/mΦyz= E→Ayz→ ==Ex.Ayz⇒Ex=93V/m=3V/mΦzx= E→Azx→ ==EyAzx⇒Ey=84V−m=2V−m∴E→=3i^+2j^+2k^V/m

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A uniform electric field $\vec{E}$ exists in a region of space. Three squares having areas 2 m², 3 m² and 4 m² lie in xy, yz and zx planes respectively. If the electric flux through the areas are 4 V-m, 9 V-m and 8 V-m respectively, then the electric field may be

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$(3 \hat{i} + 2 \hat{j} + 3 \hat{k}) \frac{V}{m}$

$(2 \hat{i} + 2 \hat{j} + 3 \hat{k}) \frac{V}{m}$

$(2 \hat{i} + 3 \hat{j} + 2 \hat{k}) \frac{V}{m}$

$(3 \hat{i} + 2 \hat{j} + 2 \hat{k}) \frac{V}{m}$

answer is D.

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Detailed Solution

$\begin{array}{l} Let the electric field be \vec{E} = (E_{x} \hat{i} + E_{y} \hat{j} + E_{z} \hat{k}) \\ Given \vec{Axy} = 2 \hat{k} m^{2}, \vec{Ayz} = 3 \hat{i} m^{2} and \vec{Azx} = 4 \hat{j} m^{2}, \\ Φ_{xy} = \vec{E} \vec{Axy} = = E_{z} . Axy \Rightarrow E_{z} = \frac{4}{2} V / m = 2 V / m \\ Φ_{yz} = \vec{E} \vec{Ayz} = = E_{x} . Ayz \Rightarrow E_{x} = \frac{9}{3} V / m = 3 V / m \\ Φ_{zx} = \vec{E} \vec{Azx} = = E_{y} Azx \Rightarrow E_{y} = \frac{8}{4} V - m = 2 V - m \\ ∴ \vec{E} = (3 \hat{i} + 2 \hat{j} + 2 \hat{k}) V / m \end{array}$