A magnetic field:
The magnetic force is given by \(F = qvB\sin\theta\). If the particle moves across the field lines, \(\sin\theta \neq 0\), resulting in a non-zero force.
If magnetic field in space is \(1\text{ T } \hat{i}\), electric field is \(10\text{ N/C } \hat{i}\), no gravitational field is present and a charged particle is released from rest from origin, it will:
Since the particle starts from rest, its initial magnetic force is zero. The electric field accelerates it along \(\hat{i}\). Because velocity remains parallel to the magnetic field, the magnetic force remains zero, and it continues on a straight line.
Statement-1: In an isolated conductor, free electrons keep on moving but no net magnetic force acts on a conductor in a magnetic field.
Statement-2: In a conductor, the average velocity of thermal motion of electrons is zero. Hence no current flows through the conductor.
The net magnetic force on a current-carrying conductor is given by \(F = I L B\). Since average velocity of thermal motion is zero, current \(I = 0\), resulting in zero net force.
If the direction of the initial velocity of a charged particle is neither along nor perpendicular to a uniform magnetic field, then the path of charged particle will be
When velocity vector is at an angle \(\theta\) (where \(0^\circ < \theta < 90^\circ\)) to the magnetic field, the component parallel to the field produces linear translation, while the perpendicular component produces circular motion. The combined path is a helix.
If a proton has velocity \((2\hat{i} + 3\hat{k})\) m/s and it is subjected to a magnetic field of \(4\hat{i}\) T, then its:
Since the magnetic force \(\vec{F} = q(\vec{v} \times \vec{B})\) is always perpendicular to the velocity, the work done is zero. Hence, the kinetic energy and speed remain constant.