As shown in figure, a cuboid lies in a region with electric field E=2 x2 hati-4 y hatj+6 hatk N / C. The magnitude of charge within the cuboid is n ϵ0 C. The value of n is (if dimension of cuboid is 1 × 2 × 3 m 3 ).

Question

As shown in figure, a cuboid lies in a region with electric field E=2 x2 hati-4 y hatj+6 hatk N / C. The magnitude of charge within the cuboid is n ϵ0 C. The value of n is (if dimension of cuboid is 1 × 2 × 3 m 3 ). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

vec E =2 x 2 hat i -4 y hat j +6 hat k <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/05cdfec4c5a18a5b10714b2b8a4d23db-.png" /> φ text net =-8 × 3+2 × 6=-12 -12=( q /ϵ0) | q |=12 ϵ0

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

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

$ϕ_{net} = - 8 \times 3 + 2 \times 6 = - 12$
$- 12 = \frac{q}{ϵ _{0}}$
$∣ q ∣ = 12 ϵ_{0}$

Q. As shown in 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 dimension of cuboid is 1×2×3m3 ).

E=2x2i^−4yj^​+6k^ ϕnet ​=−8×3+2×6=−12 −12=ϵ0​q​ ∣q∣=12ϵ0​

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

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

$ϕ_{net} = - 8 \times 3 + 2 \times 6 = - 12$
$- 12 = \frac{q}{ϵ _{0}}$
$∣ q ∣ = 12 ϵ_{0}$