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In a region, the potential is respresented by `V(x, y, z) = 6x - 8xy - 8y + 6yz`, where `V` is in volts and `x, y, z` are in meters. The electric force experienced by a charge of `2` coulomb situated at point `(1, 1, 1)` isA. `6 sqrt(5) N`B. `30 N`C. `24 N`D. `4 sqrt(35) N` |
Answer» Correct Answer - D Given, `V = 6x - 8 xy - 8 y + 6 yz` `(E_(x))_(1,1,1) = -(del V)/(dx) = -(6-8 y) = -(6-8xx1) = 2` `(E_(y))_(1,1,1) = -(del V)/(dy) = - (-8x -8 + 6z)` `= -(-8xx1-8+6xx1) = 10` `(E_(z))_(1,1,1) = -(del V)/(dz) = -(6y) = -6xx1=-6` `E = sqrt(E_(x)^(2) +E_(y)^(2) + E_(z)^(2)) = sqrt(2^(2) +10^(2) +(-6)^(2))` `= sqrt(140) = 2 sqrt(35) N//C` `F = qE = 2xx2 sqrt(35) = 4 sqrt(35) N` |
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