Consider a long thin conducting wire carrying a uniform current I. A particle having mass m and charge q is re…

Question

Consider a long thin conducting wire carrying a uniform current $I$ . A particle having mass $m$ and charge $q$ is released at a distance $a$ from the wire with a speed $v_0$ along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance $x$ from the wire. The value of $x$ is ( $\mu_0$ is the vacuum permeability):

A
$\frac{a}{2}$
B
$a \left( 1 - \frac{mv_0}{q\mu_0 I} \right)$
C
$a\,e^{-\frac{4\pi m v_0}{q\mu_0 I}}$
D
$a \left[ 1 - \frac{mv_0}{2q\mu_0 I} \right]$

Accepted Answer

C. $$a\,e^{-\frac{4\pi m v_0}{q\mu_0 I}}$$

Answer

A. $$\frac{a}{2}$$

Answer

B. $$a \left( 1 - \frac{mv_0}{q\mu_0 I} \right)$$

Answer

D. $$a \left[ 1 - \frac{mv_0}{2q\mu_0 I} \right]$$

Answer & step-by-step solution

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