Uniform magnetic fields of different strengths (B₁ and B₂), both normal to the plane of the paper exist as shown in the figure. A charged particle of mass m and charge q, at the interface at an instant moves into the region 2 with velocity v and returns to the interface. It continues to move into r…

Question

Uniform magnetic fields of different strengths (B₁ and B₂), both normal to the plane of the paper exist as shown in the figure. A charged particle of mass m and charge q, at the interface at an instant moves into the region 2 with velocity v and returns to the interface. It continues to move into region 1 and finally reaches the interface. What is the displacement of the particle during this movement along the interface? (Consider the velocity of the particle to be normal to the magnetic field and B₂>B₁)

Accepted Answer

(2) (mv)/(qB₁)(1-(B₁)/(B₂))×2. Entering normal to the interface, the particle makes a semicircle in each region and shifts by a diameter along the interface. Region 2: shift 2r₂=(2mv)/(qB₂); it then enters region 1 moving the other way, and with the same field direction it curves back: shift 2r₁=(2mv)/(qB₁) opposite to the first. Net displacement =2(r₁-r₂)=(2mv)/(qB₁)(1-(B₁)/(B₂))

Step-by-step solution

Why the other options are wrong