2. Electric Potential and Capacitance
medium

विद्युत विभव निम्न समीकरण द्वारा दिया गया है

 $V = 6x - 8x{y^2} - 8y + 6yz - 4{z^2}$

 तो मूल बिन्दु पर रखे $2\,C$ के आवेश पर लगने वाला बल......$N$ होगा

A

$2$

B

$6$

C

$8$

D

$20$

Solution

${E_x} =  – \frac{{dV}}{{dx}} =  – (6 – 8{y^2}),$${E_y} =  – \frac{{dV}}{{dy}} =  – ( – \,16xy – 8 + 6z)$

${E_z} =  – \frac{{dV}}{{dz}} =  – \,(6y – 8z)$

मूल बिन्दु पर  $x = y = z = 0$ अत:${E_x} =  – \,6,\,{E_y} = 8$ एवं ${E_z} = 0$

$E = \sqrt {E_x^2 + E_y^2}  = 10\,N/C$

अत: बल$F = QE = 2 \times 10 = 20\,N$

Standard 12
Physics

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