IIT-JEE 2008 · Paper 1 · Physics Q32

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PhysicsMultiple correct+4 / -1Question 32 of 69

A particle of mass $m$ and charge $q$ , moving with velocity $V$ enters Region II normal to the boundary as shown in the figure. Region II has a uniform magnetic field $B$ perpendicular to the plane of the paper. The length of the Region II is $\ell$ . Choose the correct choice(s).

Three regions side by side: Region I (left), Region II (a strip of width ℓ filled with crosses, i.e. a magnetic field into the page) and Region III (right). A particle moving right with velocity V enters Region II perpendicular to its left boundary.

The particle enters Region III only if its velocity

V>\dfrac{q\ell B}{m}

The particle enters Region III only if its velocity

V<\dfrac{q\ell B}{m}

Path length of the particle in Region II is maximum when velocity

V=\dfrac{q\ell B}{m}

Time spent in Region II is same for any velocity

V

as long as the particle returns to Region I

Answer and worked solution

Official answer: A, C, D

Radius of the circular path in Region II: $r=\dfrac{mV}{qB}$ .

(A) The particle crosses the strip only if $r>\ell$ , i.e. $V>\dfrac{q\ell B}m$ . True; (B) false.
(C) If $r\le\ell$ it turns back along a semicircle, path length $\pi r$ , growing with $V$ . If $r>\ell$ it leaves after an arc of angle $\theta=\sin^{-1}\frac\ell r<\frac\pi2$ , length $r\theta$ , which is less than $\pi\ell$ (it falls from $\frac\pi2\ell$ towards $\ell$ as $r$ grows). The longest path, $\pi\ell$ , is at $r=\ell$ , i.e. $V=\dfrac{q\ell B}m$ . True.
(D) A particle that returns to Region I always traces a semicircle, taking half a period $\dfrac{\pi m}{qB}$ , independent of $V$ . True.

(A), (C), (D)

Topics:Force on a moving charge

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IIT-JEE 2008 · Paper 1, Physics question 32