As shown in the figure, a cuboid lies in a region with electric field The magnitude of charge within the cuboid is . The value of is _______ (if dimensions of cuboid is ) [2023]

Question

As shown in the figure, a cuboid lies in a region with electric field $\vec{E} = 2 x^{2} \hat{i} - 4 y \hat{j} + 6 \hat{k} N/C.$ The magnitude of charge within the cuboid is $n ε_{0} C$ . The value of $n$ is _______ (if dimensions of cuboid is $1 \times 2 \times 3 m^{3}$ ) [2023]

Smart Achievers · Accepted Answer

(12)

$\vec{E} = 2 x^{2} \hat{i} - 4 y \hat{j} + 6 \hat{k}$

$ϕ_{net} = - 8 \times 3 + 2 \times 6 = - 12$

$- 12 = \frac{q}{ε_{0}} \Rightarrow$ $| q |$ $= 12 ε_{0}$

Solution

Q.
As shown in the figure, a cuboid lies in a region with electric field $\vec{E} = 2 x^{2} \hat{i} - 4 y \hat{j} + 6 \hat{k} N/C.$ The magnitude of charge within the cuboid is $n ε_{0} C$ . The value of $n$ is _______ (if dimensions of cuboid is $1 \times 2 \times 3 m^{3}$ ) [2023]

Ans.
(12)

$\vec{E} = 2 x^{2} \hat{i} - 4 y \hat{j} + 6 \hat{k}$

$ϕ_{net} = - 8 \times 3 + 2 \times 6 = - 12$

$- 12 = \frac{q}{ε_{0}} \Rightarrow$ $| q |$ $= 12 ε_{0}$

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Solution

Q. As shown in the figure, a cuboid lies in a region with electric field E→=2x2i^-4yj^+6k^ N/C. The magnitude of charge within the cuboid is nε0 C. The value of n is _______ (if dimensions of cuboid is 1×2×3 m3) [2023]

Ans. (12) E→=2x2i^-4yj^+6k^ ϕnet=-8×3+2×6=-12 -12=qε0 ⇒ |q|=12 ε0

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Q.
As shown in the figure, a cuboid lies in a region with electric field $\vec{E} = 2 x^{2} \hat{i} - 4 y \hat{j} + 6 \hat{k} N/C.$ The magnitude of charge within the cuboid is $n ε_{0} C$ . The value of $n$ is _______ (if dimensions of cuboid is $1 \times 2 \times 3 m^{3}$ ) [2023]

Ans.
(12)

$\vec{E} = 2 x^{2} \hat{i} - 4 y \hat{j} + 6 \hat{k}$

$ϕ_{net} = - 8 \times 3 + 2 \times 6 = - 12$

$- 12 = \frac{q}{ε_{0}} \Rightarrow$ $| q |$ $= 12 ε_{0}$