Question

A wire has a non-uniform cross-section as shown in figure. A steady current flows through it. The drift speed of electrons at points $P$ and $Q$ is $v_P$ and $v_Q$, respectively. Then

• A. data insufficient
• B. $v_P=v_Q$
  
• C. $v_P>v_Q$
• D. $v_P<v_Q$
  

Answer 1

The correct option is C $v_P>v_Q$

Explanation

$\to$ The current flowing is same at every cross section throughout the conductor. If any charge enters through a cross section in any part of conductor an equal amount of charge must leave out through another cross section . This is because there is no accumulation or production of charge in any part of conductor , they only continuously flow through every cross section.

$\to$ We know, $currentI=neA{v}_d$

$v_d=\frac{I}{neA}$

$n\to$ charge Carrier density ( free
electron density )

$A\to$ Area of cross-section

$v_d\to$ Drift velocity

Here $n,e$ & $I$ are constant.

So, $v_d\propto \frac{1}{A}$

Since, $A_Q>A_P$

$\Rightarrow \frac{1}{A_Q}<\frac{1}{A_P}$

Or $(v_d{)}_Q<(v_d{)}_p\Rightarrow (v{)}_Q<(v{)}_p$

Hence, option (c) is correct.