A particle of charge q , mass m enters in a region of magnetic field B with velocity V

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4.Moving Charges and Magnetism

hard

A particle of charge $q$, mass $m$ enters in a region of magnetic field $B$ with velocity $V_0 \widehat i$. Find the value of $d$ if the particle emerges from the region of magnetic field at an angle $30^o$ to its ititial velocity:-

$\frac{mv_o}{2qB}$

$\frac{mv_o}{qB}$

$\frac{mv_o}{3qB}$

$\frac{mv_o}{4qB}$

Solution

As the initial velocity of the particle is perpendicular to the field, the particle will move along the arc of a circle as shown (fig). If $r$ is the radius of the circle, then

$\frac{m v_{0}^{2}}{r}=q v_{0} B_{0} \Rightarrow r=\frac{m v_{0}}{q B_{0}}$

Also, from geometry, $L=r \sin 30^{\circ} \Rightarrow r=2 L$

or $L=\frac{r}{2}=\frac{m v_{0}}{2 q B_{0}}$

Standard 12

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easy

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(JEE MAIN-2022)

A particle of charge $q$, mass $m$ enters in a region of magnetic field $B$ with velocity $V_0 \widehat i$. Find the value of $d$ if the particle emerges from the region of magnetic field at an angle $30^o$ to its ititial velocity:-

Solution

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