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In a region, the potential is represente...

In a region, the potential is represented by `V(x, y, z) = 6x - 8xy - 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

A

`6sqrt(5)N`

B

`30 N`

C

`24 N`

D

`4sqrt(35)N`

Text Solution

Verified by Experts

The correct Answer is:
D
We know,
`vec(E ) = E_(x)hat(i)+E_(y)hat(j)+E_(z)hat(k) = -(dV)/(dx)hat(i) - (dV)/(dy)hat(j) - (dV)/(dz)hat(k)`
Now, `V(x,y,z) = 6x - 8xy - 8y + 6yz`
`:. (dV)/(dx) = 6 - 8y , (dV)/(dy) = -8x - 8 + 6z , (dV)/(dy) = 6y`
`:. vec(E ) = -(6-8y)hat(i) -(-8x-8+6z)hat(j)-6yhat(k)`
`:.` Electric field at point (1,1,1)
`vec(E ) = -(6-8xx1)hat(i)-(-8xx1-8+6xx1)hat(j)-(6xx1)hat(k)`
`2hat(i) + 10 hat(j) - 6hat(k)`
`E = sqrt(2^(2)+10^(2)+(-6)^(2)) = sqrt(140) = 2sqrt(35)`
`:.` Force acting on charge 2C,
`F = qE = 2 xx 2sqrt(35) = 4sqrt(35)N`.
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