Question

1. A point object is placed at the center of a glass sphere of radius R. Refractive index of Glass is μ. Where is the image of the point object formed? Real or virtual?

2. An electron is moving with a uniform speed u along the positive x axis. At y = 0, the electron enters a region of uniform magnetic field $\vec{B} = - B_0 \hat{k}$ (where k = unit vector along z axis). Magnetic field B exists to the right of y axis. The electron exits from the region after some time with speed v at coordinate y. Then y is positive or negative and why?

Answer 1

1. The light rays emanating from the object at the center of the sphere pass radially out of the sphere.  Radius is normal to the surface.  So angle of incidence and refraction are both 0.  So All the rays appear to diverge from the center C.  A virtual image is formed at the center of the sphere.

2. 
$\vec{v_e} = - v_0 \hat{i},\ \ \ \hat{B}= - B_0\ hat{k}\\\\\vec{F}=electromagnetic\ force\ on\ moving\ e=(-e)\ \vec{v} \times \vec{B}\\\\= - e v_0 B_0 \hat{j}$

     Thus the electron makes a circle, as the force and the acceleration on it are always perpendicular to the magnetic field and the velocity.  The force is the centripetal force.  As the force is in the - Y direction, e makes a semi circle on the -Y axis.

     m v²₀ / R = e v₀ B₀ 

     R = m v₀² / (e v₀ B₀)

The electron touches the y axis at  -2 R.