(a) A charged particle enters at right angles into a uniform magnetic field as shown. What should be the nature of a charge on the particle if it begins to move in a direction pointing vertically out of the page due to its interaction with the magnetic field?

(b) Between which two points of a concave mirror should an object be placed to obtain a magnification of, −3?
(c) "The refractive index of carbon disulphide is 1.63". What is the meaning of this statement in relation to the speed of light?

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Solution

(a) When a charged particle enters at right angles into a uniform magnetic field, it feels a force, $F = q (v \times B)$ , also known as Lorentz force. Here, q is the charge of the particle, v is it's velocity vector and B is the magnetic field strength vector in that region.

Clearly, the direction of the force is perpendicular to both, the velocity vector and the magnetic field strength vector. In the given case, the cross product of velocity and magnetic field points vertically out of the page. The direction of charge is also given the same. Hence, the charged particle is positive in nature.

(b) The object should be placed between the focus and radius of curvature of the concave mirror. Then it will form an inverted and enlarged image. In that case, a magnification of '-3' can be obtained.

(c) Refractive index of a medium is the measure of the speed of light in that, medium with respect to the vacuum. It is defined as the ratio of the speed of the light in a vacuum to the speed of the light in the given medium. So, "The refractive index of carbon disulphide is 1.63" means that the speed of light in carbon disulphide is $\frac{1}{1.63}$ times the speed of the light in vacuum.

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