Q18 of 31 Page 170

Answer the following questions:

A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?

When a charged particle enters a magnetic field it experiences a force known as Magnetic Lorentz Force which is given by:



Where is the force on the Charged particle having charge q,moving with a velocity in a magnetic Field


Note: , and are vector quantities, and charge q is a scalar quantity, and is the cross product or vector product of and , so resultant is perpendicular to plane containing and


if we evaluate the formula we get,



Where, and are magnitude of velocity and magnetic field respectively, θ is the angle between Velocity of particle and magnetic field and ŵ is a unit vector perpendicular to plane containing and


When angle between Velocity of particle and magnetic field is either or i.e. particle is either moving parallel or antiparallel to the field we can see force on the particle,


F = 0 N, since sinθ = 0 when θ is either 00 or 1800,


The particle came out of the magnetic field un-deflected, and with constant velocity i.e. it did not experience any force so we can say that particle was moving in same direction as that of magnetic field i.e. from East Towards West or in opposite direction from West towards East and magnitude of velocity can be any value.


The following figure depicts both the situations



More from this chapter

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16

For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by,


(a) Show that this reduces to the familiar result for field at the centre of the coil.


(b) Consider two parallel co-axial circular coils of equal radius R, and number of turns N, carrying equal currents in the same direction, and separated by a distance R. Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to R, and is given by,


, approximately.


[Such an arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils.]

 17

A toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 3500 turns of a wire are wound.

If the current in the wire is 11 A, what is the magnetic field


(a) outside the toroid,


(b) inside the core of the toroid, and


(c) in the empty space surrounded by the toroid.

 18

Answer the following questions:

A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?

 18

Answer the following questions:

An electron travelling west to east enters a chamber having a uniform electrostatic field in north to south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting from its straight line path.