એક સમાન વિદ્યુત ક્ષેત્ર \(\overrightarrow{ E }=3 \times 10^3 \hat{k} NC ^{-1}\) નો વિચાર કરો. 20 cm બાજુવાળા એક ચોરસમાંથી પસાર થતું, જેનું સમતલ \(yz\) સમતલને સમાંતર છે, આ ક્ષેત્રનું વિદ્યુત ફ્લક્સ ________ \(Nm ^2 C ^{-1}\) છે.

A શૂન્ય
B 90
C 60
D 120

Verified Solution

Answer & Solution

Correct Answer

(A) શૂન્ય

Step-by-step Solution

Detailed explanation

(A)
ચોરસનું ક્ષેત્રફળ
\(\begin{array}{l}
A=\left(20 \times 10^{-2}\right)^2 \\
A=400 \times 10^{-4} \hat{i} m^2
\end{array}
\)
ફ્લક્સ \(\phi=\overrightarrow{ E } \cdot \overrightarrow{ A }\)
\(\begin{array}{l}\phi=\left(3 \times 10^3\right) \hat{k} \\ \quad\left(400 \times 10^{-4}\right) \hat{i} \\ \phi=0 \quad(\hat{k} \cdot \hat{i}=0)\end{array}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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