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Question

# In a certain region of space, the potential is given by V=k[2x2−y2+z2]. The electric field at the point(1,1,1) has magnitude :2k√62k√3k√64k√3

A
k6
B
2k3
C
4k3
D
2k6
Solution
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#### Given, V=k[2x2−y2+z2]Electric field , →E=−(dVdx^i+dVdy^j+dVdz^k)or,→E=−k(4x^i−2y^j+2z^k)or,→E(1,1,1)=−k(4^i−2^j+2^k)Magnitude of electric field=|→E(1,1,1)|=√k2(16+4+4)=k√24=2k√6

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