IIT-JEE 2007 · Paper 2 · Physics Q8

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PhysicsSingle correct+3 / -1Question 8 of 66

A magnetic field $\vec B=B_0\hat j$ exists in the region $a<x<2a$ and $\vec B=-B_0\hat j$ , in the region $2a<x<3a$ , where $B_0$ is a positive constant. A positive point charge moving with a velocity $\vec v=v_0\hat i$ , where $v_0$ is a positive constant, enters the magnetic field at $x=a$ . The trajectory of the charge in this region can be like,

Graph of the field's y-component against x: B = +B₀ for a < x < 2a and B = −B₀ for 2a < x < 3a, zero elsewhere.

z against x: the path leaves the x-axis at x = a curving upward (concave up) until x = 2a, then bends the other way (concave down) and is still rising at 3a.

z against x: the path leaves the x-axis at x = a curving downward until 2a, then bends back and is still going down at 3a (mirror image of A).

z against x: the path rises from x = a to a cusp at x = 2a and comes back down to the axis at x = 3a.

z against x: the path dips below the axis from x = a to a cusp at x = 2a and returns to the axis at x = 3a.

Answer and worked solution

Official answer: A

Force at entry. $\vec F=q\vec v\times\vec B=qv_0B_0(\hat i\times\hat j)=qv_0B_0\hat k$ : the charge starts to curve towards $+z$ , on a circular arc in the x-z plane.

Second region. $\vec B$ reverses, so the force turns the other way and the path bends back, curving the opposite way while still moving up and to the right: an S-shaped path rising above the x-axis.

(A)

Topics:Force on a moving charge

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IIT-JEE 2007 · Paper 2, Physics question 8