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An electric charge `2 xx 10^(-8) C` is placed at the point `(1,2,4)`. At the point `(3,2,1)` , the electric (i) potential will be `50 V` (ii) field will have no `Y`-component (iii) field will increase by a factor `K` if the space between the points is filled with a dielectric of constant `K` (iv) field will be along `Y`-axisA. field will increase by a factor K if the space between the points is filled with a dielectric of dielectric constant KB. field will be along the y-axis.C. potential will be 49.9 V.D. field will have no y-components. |
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Answer» Correct Answer - C::D c.,d. `vecr_(p)=hati+2hatj+4hatk,vecr_(q)=3hati+2hatj+hatk` `[vecr_(q)-vecr_(p)]=sqrt((2)^(2)+(-3)^(2))=sqrt(13)` As `q=2xx10^(-8)C`, `V=(1)/(4piepsilon_(0))(q)/([vecr_(q)-vecr_(p)])` `=(9xx10(9)xx2xx10^(-8))/(sqrt(13))=49.9V` `vecE=(1)/(4piepsilon_(0))(q)/([vevr_(q)-vecr_(p)]^(2))((vecr_(q)-vecr_(p)))/([vecr_(q)-vecr_(p)])` `=(1)/(4piepsilon_(0))(q)/([vecr_(q)-vecr_(p)]^(3))(2hati-3hatk)` (By filling a dielectric of dielectric constant `K`, electric field gets decreases as `E=E_(0)//K` and `Kgt1`) |
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