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The vector form of Coulomb's law is (A) ...

The vector form of Coulomb's law is (A) `vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(|vec r|^(3))vec r` (B) `vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(r^(3))` (C) `vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(r^(2))vec r` (D) `vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(r)vec r`

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Step by step text solution for The vector form of Coulomb's law is (A) vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(|vec r|^(3))vec r (B) vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(r^(3)) (C) vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(r^(2))vec r (D) vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(r)vec r by PHYSICS experts to help you in doubts & scoring excellent marks in Class 9 exams.

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The vector form of Coulomb's law is (A) vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(|vec r|^(3))vec r (B) vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(|vec r|^(3)) (C) vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(r^(2))vec r (D) vec F=(1)/(4 pi epsilon_(0))*(q_(1)q_(2))/(r)vec r

[" Two uniformly charged non "],[" conducting spheres of radii "R_(1)" and "],[R_(2)" having charges "Q_(1)" and "Q_(2)],[" respectively are seperated by "],[" distance "r" .Total electrostatic "],[" energy of this system is "],[qquad [U=(1)/(4 pi epsilon_(0)){(3Q_(1)^(2))/(5R_(1))+(3Q_(2)^(2))/(5R_(2))+(Q_(1)Q_(2))/(r)}],[U=(1)/(4 pi epsilon_(0)){(3Q_(1)^(2))/(5R_(1))+(3Q_(2)^(2))/(5R_(2))-(Q_(1)Q_(2))/(r)}],[U=(1)/(4 pi epsilon_(0)){(Q_(1)^(2))/(5R_(1))+(3Q_(2)^(2))/(5R_(2))-(Q_(1)Q_(2))/(r)}],[U=(1)/(4 pi epsilon_(0)){(3Q_(1)^(2))/(5R_(1))+(3Q_(2)^(2))/(R_(2))+(Q_(1)Q_(2))/(r)}]]

Knowledge Check

  • The Bohr model for the H-atom relies on the Coulomb's law of electrostatics . Coulomb's law has not directly been varified for very short distances of the order of angstroms. Suppos-ing Coulomb's law between two oppsite charge +q_(1),-q_(2) is modified to |vec(F)|=(q_(1)q_(2))/((4piepsilon_(0))r^(2))1/r^(2),rgeR_(0) =(q_(1)q_(2))/((4piepsilon_(0))r^(2))1/R_(0)^(2)(R_(0)/r)^(epsilon), rleR_(0) Calculate in such a case , the ground state enenergy of H-atom , if epsilon 0.1,R_(0)=1Å

    A
    `-11.4eV`
    B
    `-7.9eV`
    C
    `-13.1eV`
    D
    `-15.2eV`

  • A conducting sphere A of radius a , with charge Q , is placed concentrically inside a conducting shell B of radius b . B is earthed. C is the common center of A and B . Study the following statements. (i) The potential at a distance r from C , where a le r le b, is (1)/(4 pi epsilon_0)(q/( r)) (ii) The potential difference between A and B is (1)/(4 pi epsilon_0) Q ((1)/( r) - (1)/B) (iii) The potential at a distance r from C , where a le r le b, is (1)/(4 pi epsilon_0) Q ((1)/r - (1)/B) Which of the following statements are correct ? .

    A
    Only (i) and (ii)
    B
    Only (ii) and (iii)
    C
    Only (i) and (iii)
    D
    All of these

  • if vec(P) xx vec(R ) = vec(Q) xx vec(R ) , then

    A
    `vec(P) = vec(Q)`
    B
    `vec(P)` and `vec(Q)` need not be equal
    C
    There are infinite number of possibilities for `vec(P)` (If `vec(Q)` and `vec(R )` are given ) which satisfy this relationship.
    D
    `vec(p)` and `vec(Q)` must be coplanar

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    41.Self energy of conducting sphere of radius r carrying charge is (1) (Q^(2))/(8 pi epsilon_(0)(r) (2) (Q^(2))/(4 pi epsilon_(0)(r) (3) (Q^(2))/(6 pi epsilon_(0)(r) (4) (Q^(2))/(2 pi epsilon_(0)(r)

    A charge q_(1) is placed at the centre of a spherical conducting shell of radius "R" .Conducting shell has a total charge q_(2) .Electrostatic potential energy of the system is (A) (q_(1)^(2)+2q_(1)q_(2))/(8 pi varepsilon_(0)R) (B) (q_(2)^(2)+2q_(1)q_(2))/(8 pi varepsilon_(0)R) (C) (q_(1)^(2)+q_(1)q_(2))/(8 pi varepsilon_(0)R) (D) (q_(2)^(2)+q_(1)q_(2))/(8 pi varepsilon_(0)R)

    The Bohr model for the H-atom relies on the Coulomb's law of electrostatics. Coulomb's law has not directly been verified for very short distances of the order of angstroms. Supposing Coulomb's law between two opposite charge +q_(1), -q_(2) is modified to |vecF|=(q_(12))/((4piepsilon_(0))) 1/(r^(2)) , rgeR_(0) =(q_(1)q_(2))/((4piepsilon_(0))) 1/(R_(0)^(2)) ((R_(0))/r)^(epsilon) , rleR_(0) Calculate in such a case, the ground state energy of a H-atom, if epsilon=0.1, R_(0)=1Å .

    There are three charges Q_(1) columb Q_(2) columb and Q_(3) columb. Q_(2) and Q_(3) are fixed at positive (0 0) and (30 0) respectively.Now Q_(1) moves in circular path in x -y plane of radius 40 cm with help of external agent starting from (0 40) about origin then work done by external agent is till Q_(1) crosses x axis (40 0) given co-ordinates are in centimeters: 1) (Q_(1)Q_(3))/(4 pi epsilon_(0)) joule 2) (Q_(1)Q_(3))/(2 pi epsilon_(0)) joule 3) (2Q_(1)Q_(3))/(pi epsilon_(0)) joule 4) (2Q_(1)(Q_(2)+Q_(3)))/(pi epsilon_(0)) joule

    There are three charges Q_(1) columb Q_(2) columb and Q_(3) columb. Q_(2) and Q_(3) are fixed at positive (0,0) and (30,0) respectively.Now Q_(1) moves in circular path in x -y plane of radius 40 m with help of external agent starting from (0 ,40) about origin then work done by external agent is till Q_(1) crosses x axis (40, 0) given co-ordinates are in centimeters: (1) (Q_(1)Q_(3))/(4 pi epsilon_(0)) joule (2) (Q_(1)Q_(3))/(2 pi epsilon_(0)) joule (3) (2Q_(1)Q_(3))/(pi epsilon_(0)) joule (4) (2Q_(1)(Q_(2)+Q_(3)))/(pi epsilon_(0)) joule

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