Question
Download Solution PDFयदि किसी बिंदु पर विभव V = x (y2 - 4x2) द्वारा दिया जाता है, तो बिंदु पर विद्युत क्षेत्र के कार्तीय घटकों की गणना करें।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया:
V = x (y2 - 4x2)
संकल्पना:
विभव फलन से विद्युत क्षेत्र की गणना करने के लिए, हम क्रमशः x, y और z के सापेक्ष आंशिक अवकलज का उपयोग करते हैं।
सूत्र:
Ex = -δV/δx,
Ey = -δV/δy,
Ez = -δV/δz
जहाँ δy/δx का अर्थ है अन्य चरों को स्थिर मानकर x के सापेक्ष आंशिक अवकलज ।
गणना:
V = x (y2 - 4x2)
⇒ V = xy2 - 4x3
• Ex = -δV/δx
⇒ Ex = \(-\frac{\delta(xy^2 - 4x^3) }{\delta x}\)
= -(y2 - 12x2)
= 12x2 - y2
• Ey = -δV/δy
⇒ Ex = \(-\frac{\delta(xy^2 - 4x^3) }{\delta y}\)
= -2x
• Ez = \(-\frac{\delta(xy^2 - 4x^3) }{\delta z}\)
= 0
∴ Ex = 12x2 - y2, Ey = -2xy, Ez = 0
Last updated on Jun 19, 2025
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