If potential (in volts) in a region is expressed as V(x, y, z) =  6xy – y + 2yz , the electric field (in N/C) at point (1,1,0) is

If potential (in volts) in a region is expressed as V(x, y, z) =  6xy - y + 2yz , the electric field (in N/C) at point (1,1,0) is

  1. A

    -(2i^+3j^+k^)

  2. B

    -(6i^+9j^+k^)

  3. C

    -(3i^+5j^+3k^)

  4. D

    -(6i^+5j^+2k^)

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    Solution:

    The electric field E and potential V in a region are related as

    E=-Vxi^+Vyj^+Vzk^

     Here, V(x,y,z)=6xy-y+2yz

     E=-x(6xy-y+2yz)i^+y(6xy-y+2yz)j^+z(6xy-y+2yz)k^

    =-[(6y)i^+(6x-1+2z)k^+(2y)k^]

     At point (1,1,0)

    E=-[(6(1))i^+(6(1)-1+2(0))j^+(2(1))k^]

    =-(6i^+5j^+2k^)

     

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