positive charge moving with initial velocity v in a uniform magnetic fieldB experiences a magnetic force F. Which of the following statements is/are ALWAYSTRUE?I. v has no component parallel to F.II. B has no component parallel to v.III. F has no component parallel to B.
Question
positive charge moving with initial velocity v in a uniform magnetic fieldB experiences a magnetic force F. Which of the following statements is/are ALWAYSTRUE?I. v has no component parallel to F.II. B has no component parallel to v.III. F has no component parallel to B.
Solution
The Lorentz force law states that the force (F) on a particle of charge q moving with velocity v in the presence of an electric field E and a magnetic field B is given by F = q(E + v × B).
I. v has no component parallel to F. This statement is TRUE. The force exerted by a magnetic field on a moving charge is always perpendicular to the direction of motion. This is because the magnetic force is the cross product of velocity and magnetic field (F = qv × B), and the result of a cross product is always perpendicular to the input vectors.
II. B has no component parallel to v. This statement is FALSE. The magnetic field can have a component parallel to the velocity of the charge. However, only the component of the velocity perpendicular to the magnetic field will contribute to the magnetic force.
III. F has no component parallel to B. This statement is TRUE. As mentioned in the explanation for statement I, the magnetic force is always perpendicular to the direction of the magnetic field because it is a result of the cross product of velocity and magnetic field.
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