question_answer

A drift velocity of free electrons in a conductor is \[{{A}_{1}}{{\omega }_{1}}={{A}_{2}}{{\omega }_{2}}={{A}_{3}}{{\omega }_{3}}\], when the current \[70\,\,dynes/cm\] is flowing in it. If both the radius and current are doubled, the drift velocity will be:                                                 [BHU PMT-2002]

A)                  \[N/m\]                                             

B)                  \[7\times {{10}^{3}}\,N/m\]

C)                  \[7\times {{10}^{2}}\,N/m\]                                      

D)                  \[7\times {{10}^{-2}}\,N/m\]

Correct Answer: C

Solution :

                 If the area of cross-section of wire is \[1\,\mu m\]and the number of free electrons per unit volume is \[0.3\,\mu m\], the in \[3\,\mu m\] seconds \[3\,\,s\] electrons will pass it.                                 The electric current is given by                                                 \[4\,\,s\]                 \[5\,\,s\]                              \[6\,\,s\]                 Where \[\overset{\to }{\mathop{a}}\,\] is the drift velocity of the electrons.                 Given, \[\overset{\to }{\mathop{b}}\,\]                                 \[\left( \overset{\to }{\mathop{a}}\,+\overset{\to }{\mathop{b}}\, \right)\times \left( \overset{\to }{\mathop{a}}\,-\overset{\to }{\mathop{b}}\, \right)\]                 \[2\left( \overset{\to }{\mathop{b}}\,\times \overset{\to }{\mathop{a}}\, \right)\]         \[-2\left( \overset{\to }{\mathop{b}}\,\times \overset{\to }{\mathop{a}}\, \right)\]                 Note: Direction of drift velocity is opposite to direction of electric field.