A magnetic field $\vec{B}=B_{0} \hat{j}$ exists in the region $a<x<2 a$ and $\vec{B}=-B_{0} \hat{j}$, in the region $2 a<x<3 a$, 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,

JEE Advanced · 2007 · 08 Apr 2007 · Paper 2 · Magnetic Effects of Current

A magnetic field

B = B_{0} \hat{j}

exists in the region

a < x < 2 a

and

B = - B_{0} \hat{j}

, in the region

2 a < x < 3 a

, where

B_{0}

is a positive constant. A positive point charge moving with a velocity

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,

(A)(see structure)
✓ Correct
(B)(see structure)
(C)(see structure)
(D)(see structure)

Answer: (A)

Solution

The Lorentz force on the charge is

F = q v \times B

Region 1 (

a < x < 2 a

B = B_{0} \hat{j}

F = q (v_{0} \hat{i}) \times (B_{0} \hat{j}) = q v_{0} B_{0} (\hat{i} \times \hat{j}) = q v_{0} B_{0} \hat{k}

(upward)
The particle curves upward (concave upward path).

Region 2 (

2 a < x < 3 a

B = - B_{0} \hat{j}

F = q (v_{0} \hat{i}) \times (- B_{0} \hat{j}) = - q v_{0} B_{0} \hat{k}

(downward)
The particle curves downward (concave downward path).

The trajectory shows an upward arc in the first region followed by a downward arc in the second region, matching option (A).

JEE Advanced · 2007 · 08 Apr 2007 · Paper 2 · Single correct option

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JEE Advanced · 2007 · 08 Apr 2007 · Paper 2 · Magnetic Effects of Current

Solution

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