1.

At a distance r from a point located at origin in space, the electric potential varies as `V= 10r`. Find the electric field at `vecr = 3hati + 4 hatj - 5hatk`.A. `(sqrt2)(3hati+4hatj-5hatk)`B. `(-sqrt2)(3hati+4hatj-5hatk)`C. `(-sqrt3)(3hati+4hatj-5hatk)`D. none of these

Answer» Correct Answer - B
`V=10r=10sqrt(x^(2)+y^(2)+z^(2))`
`E_(x)=-(dv)/(dx)=-(10(2x))/(2sqrt(x^(2)+y^(2)+z^(2)))`
`=(-10x)/(sqrt(x^(2)+y^(2)+z^(2)))=(10xx3)/(sqrt(3^(2)+4^(2)+5^(2)))=-3sqrt(2)`
similarly
`E_(y)=-4sqrt(2)`
`E_(x)=5sqrt(2),ver(E)=E_(x)hat(i)+E_(y)hat(j)+E_(z)hat(k)`


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