Question

• Based on your experimental observations, data, graphs, and conclusions discuss the behavior of a charged particle in a magnetic field. Be sure to use your information from each part of the experiment.
• State the formula for the force on a charge in a magnetic field.
• With the exception of compasses, you seldom see or personally experience forces due to the Earth’s small magnetic field. To illustrate this, suppose that in a physics lab you rub a glass rod with silk, placing a 20-nC positive charge on it. Calculate the force on the rod due to the Earth’s magnetic field, if you throw it with a horizontal velocity of 10 m/s due west in a place where the Earth’s field is due north parallel to the ground
• If a charged particle moves in a straight line through some region of space, can you say that the magnetic field in that region is necessarily zero? Explain your answer.
• A cosmic ray proton moving toward the Earth at 5.00 × 107 experiences a magnetic force of 1.70 × 10−16 N. What is the strength of the magnetic field if there is a 45º angle between it and the proton’s velocity? Is this value consistent with the known strength of the Earth’s magnetic field on its surface? Discuss.

Answer 1

(a) It is the case of Lorentz Magnetic force acting on a charged particle of charge 'Q' ,moving with velocity 'v', in magnetic field of strength, 'B' and this force is given by,

..............(i), (letters in bold represents the vector quantities, F, v and B)

(b) In the image, as shown below

Assuming, vertically upward as positive y-axis ( +j)

  vertically downward as negative y-axis (-j)

North as negative Z-axis (-k)

South as positive Z-axis (+k)

East as positive X-axis (+i)

west as negative X-axis (-i)

1.)

2.)

(c) If a charged particle is moving with a certain velocity 'v' in a region, it is not necessary that the magnetic field must be zero if it travels its path in a straight line, without getting deflected, i.e., doesn't experience any Lorentz magnetic force.

From equation (i), it is clear that the Lorentz magnetic force acts on the charged particle only when its velocity and magnetic field in which it is moving are normal to each other or at some angle.

If the directions of velocity and the magnetic field are same, i.e either parallel or anti-parallel, in those cases, the moving charged particle will not get deflected or we can say that the Lorentz magnetic force is zero.

And if magnetic field strength is zero, in this situation too, Lorents magnetic force will not act on the charged particle.

Thus, it is not necessarily true that the magnetic field must be zero in a region if a charged particle is moving in a straight line in that region.

(d)

This calculated value of the magnetic field is not consistent as it varies from one point to another on the Earth's surface, i.e., varies from poles to equator.