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Two point charges q(1) , q(2) initially ...

Two point charges `q_(1) , q_(2)` initially at infinity are brought one by one points `P_1` and `P_2` specified by position vectors `r_1` and `r_2` , relative to some origin . What is the potential energy of this energy configuration ?

Text Solution

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The potential energy of the given charge configuration is `U = (1)/(4 pi in_(0)) * (q_(1) q_(2))/(|vecr_(2) - vecr_(1)|)`
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Knowledge Check

  • Let the points P, Q and R have position vectors r_(1) = 3i-2j-k r_(2) =i+3j+4k and r_(3) =2i+j-2k relative to an origin O. The distance of P from the plane OQR is

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  • Two point charges q_1 and q_2 are placed in an external uniform electric field as shown in figure. The potential at the location of q_1 and q_2 are V_1 and V_2 , i.e., V_1 and V_2 are potentials at location of q_1 and q_2 due to external unspecified charges only. Then electric potential energy for this configuration of two charged particle is

    A
    `(q_1V_1+q_2V_2)/2`
    B
    `q_1V_1 + q_2V_2`
    C
    `q_1V_1+q_2V_2+(q_1q_2)/(4piepsilon_0r)`
    D
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  • The positions of two point charges q_(1) and q_(2) are vecr_(1) and vecr_(2) , respectively. Find the position of the point where the net field is zero due to thses charges.

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    `(vecr_(1)sqrt(q_(1))+vecr_(2)sqrtq_(2))/(sqrtq_(1)+sqrtq_(2))`
    B
    `(vecr_(1)sqrt(q_(2))+vecr_(2)sqrtq_(1))/(sqrtq_(1)+sqrtq_(2))`
    C
    `(vecr_(1)sqrt(q_(2))+vecr_(2)sqrtq_(1))/(sqrt(q_(1)+q_(2)))`
    D
    `(vecr_(1)sqrt(q_(1))+vecr_(2)sqrtq_(2))/(sqrt(q_(1)+q_(2)))`

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