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Electric Charges And Fields

Question
CBSEENPH12039864
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In a region, the potential is represented by V (x,y,z) = 6x - 8 xy - 8y + 6yz, where V is in volts and x, y, z are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1,1,1) is,

  • 6 square root of 5 N

  • 30 N

  • 24 N

  • 4 square root of 35 N

Solution

D.

4 square root of 35 N

We know,
F = qE          ... (i)
E = negative dV over dr
straight E subscript straight x space equals space δV over δx equals 6 minus 8 straight y straight E subscript straight y space equals space δV over δy space equals space minus 8 straight x space minus space 8 space plus space 6 straight z straight E subscript straight z space equals space 6 space straight y    ... (ii)
The values of Ex, Ey and Ez at (1,1,1) are
Ex = 6 - 8x(1) = -2
Ey = -8(1) - 8 + 6(1) = -10
Ez = 6 x 1 = 6
Therefore,
 straight E subscript net space equals space square root of left parenthesis negative 2 right parenthesis squared plus left parenthesis 10 right parenthesis squared plus left parenthesis 6 right parenthesis squared end root space space space space space space space space equals space square root of 4 space plus 100 space plus space 36 end root space space space space space space space space equals square root of 140 space space space space space space space space equals space square root of 35 space straight x space 4 end root space space space space space space space space equals space 2 square root of 35 space straight N divided by straight C So comma space straight F space equals space qE subscript net space space space space space space space space space space space equals space 2 left parenthesis 2 square root of 35 right parenthesis space space space space space space space space space space equals space 4 square root of 35 space straight N

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point? 

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