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`

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)}]]

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 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

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

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 ? .

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