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The direction (theta) of vec(E) at point...

The direction `(theta)` of `vec(E)` at point P due to uniformly charged finite rod will be

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The correct Answer is:
A, B, C, D
(A) Let `hati and hatj` be the unit vectors along OX and OY respectively.
Now, OP=3 and `anngleXOP=45^(@)` implies that
`OP=(3cos45^(@))hati+(3sin45^(@))hatj=(3)/(sqrt(2))(hati+hatj)`
(B) Again `angleXOR=135^(@) and OR=4` implies that
`OR=(4)/(sqrt(2))(-hati+hatj)=2sqrt(2)(-hati+hatj)`
(C) the position vector of Q is given by
`OP+PQ=OP+OR=(1)/(sqrt(2))(-hati+7hatj)`

`thereforeOM=(((3)/(sqrt(2)))(hati+hatj)+((1)/(sqrt(2)))(-hati+7hatj))/(2)`
`=(2hati+10hatj)/(2sqrt(2))=(hati+5hatj)/(sqrt(2))`
(D) Now, `PT:RT=1:2`
thereofore, `OT=(1(OR)+2(OP))/(3)`
`=(((4)/(sqrt(2)))(-hati+hatj)+2[((3)/(sqrt(2)))(hati+hatj)])/(3)`
`=(sqrt(2))/(3)(hati+5hatj)`
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