Question

(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?"

Answer 1

Explanation:

(a) When a charged particle enters a stable magnetic field at a right angle, it undergoes a force $F = q (v \times B),$ also known as the Lorentz force.

• The direction of the force perpendicular to both is the velocity vector and the magnitude vector of that  magnetic field.
• In that case, the cross product of velocity and magnetic field indicates vertically out of the page. Therefore, the charged particle has a positive nature.

(b) The object must lie between the radius of curvature of that concave mirror and the focus .Then it forms an inverted and enlarged image. In this case, a magnification of "-3" is obtained.

(c) Refractive Index: It is defined as the ratio between the speed of light in a vacuum and the speed of light in a given environment.

Thus, the "refractive index of the carbon disulphide is 1.63 times", which means that the light's speed in carbon disulphide is $\frac{1}{1.63}$ times the speed of light in the vacuum.

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