Title 01. Electric Charges and Fields.pdf ✅

01. ELECTRIC CHARGES and FIELDS #QID# 5453 (1.) A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre (a.) decreases as r increases for r R  and for r R  (b.) increases as r increases for r R  and for r R  (c.) zero as r increases for r R  , decreases as r increases for r R  (d.) zero a sr increases for r R  , increases as r increases for r  R (NEET2019) Ans: c Exp: (c) : In a uniformly charged hollow conducting sphere, (i) For r R E  = , 0 (ii) For 0 1 , ˆ 4 Q r R E r  r  = ; E decreases #QID# 5454 (2.) Two point charges A and B, having charges + Q and −Q respectively, are placed at certain distance apart and force acting between them is F. If 25% charge of A is transferred to B , then force between the charges becomes (a.) 4 3 F (b.) F (c.) 9 16 F (d.) 16 9 F (NEET 2019) Ans: c Exp: (c) : In case I: 2 2 0 1 4 Q F  r = − (i) In Case II: 4 A Q Q Q= − , 4 B Q Q Q = − + 2 0 1 4 4 4 Q Q Q Q F  r         − − +       = 2 2 2 0 0 3 3 1 1 9 4 4 4 4 16 Q Q Q   r r     −         = = − (ii) From equations (i) and (ii), 9 16 F F  =
#QID# 5455 (3.) Two parallel infinite line charges with linear charge densities + C m/ and −C m/ are placed at a distance of 2R in free space. What is the electric field mid‐way between the two line charges?. (a.) 0 / 2 N C R   (b.) zero (c.) 0 2 N C/ R   (d.) 0 N C/ R   (NEET 2019) Ans: d Exp: (d): Electric field due to an infinite line charge, 0 2 E r   = Net electric field at mid‐point O, E E E = + As, 1 2 0 2 E E R   = = 1 0 1 0 E E NC 2 R   −  = = #QID# 5458 (4.) An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E . The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance h . The time of fall of the electron, in comparison to the time of fall of the proton is (a.) smaller (b.) 5 times greater (c.) 10 times greater (d.) equal(NEET 2018) Ans: a Exp: (a): Force experienced by a charged particle in an electric field, F qE = As F ma = qE ma qE a m  =  = (i) As electron and proton both fall from same height at rest. Then initial velocity = 0 From 1 2 2 s ut at = + ( 0 u = )

(6.) Suppose the charge of a proton and an electron differ slightly One of them is −e, the other is (e e + ) . If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then e is of the order of [Given: mass of hydrogen 27 1.67 10 ] m kg h − =  (a.) 23 10 C − (b.) 37 10 C − (c.) 47 10 C − (d.) 20 10 C − (NEET 2017) Ans: b Exp: (b): A hydrogen atom consists of an electron and a proton.  Charge on one hydrogen atom = + = − + +  =  q q e e e e e p ( ) Since a hydrogen atom carry a net charge e Electrostatic force, 2 2 1 ( ) 4 e o e F  d  = (i) will act between two hydrogen atoms. The gravitational force between two hydrogen atoms is given as 2 h h g Gm m F d = (ii) Since, the net force on the system is zero, F F e g = Using eqns. (i) and (ii), we get 2 2 2 2 0 ( ) 4 Gmh e  d d  = 2 2 0 ( ) 4 h  = e Gm  ( ) 11 27 2 9 6.67 10 (1.67 10 ) 9 10 − − =      37 e C 10−  = #QID# 5464 (7.) An electric dipole is placed at an angle of30o with an electric field intensity 5 1 2 10 . NC−  It experiences a torque equal to 4Nm . The charge on the dipole, if the dipole length is 2 cm, is (a.) 8mC (b.) 2mC (c.) 5mC (d.) 7C (NEET ‐II 2016) Ans: b Exp: (b): Here, 5 1 30 , 2 10 o E NC−  = =   = = = = 4 , 2 0.02 , Nm l cm m q ?.  =  =  pE ql E sin sin ( )