`color{blue} ✍️` Let us suppose that there is a point charge `q` (moving with a velocity `v` and, located at `r` at a given time `t` ) in presence of both the electric field `E (r)` and the magnetic field `B (r)`. The force on an electric charge q due to both of them can be written as
`color{navy}(F = q [ E (r) + v × B (r)] ≡ F_("electric") +F_("magnetic")).........(4.3)`
`color{blue} ✍️` This force was given first by H.A. Lorentz based on the extensive experiments of Ampere and others. It is called the Lorentz force.
`color{blue} ✍️` You have already studied in detail the force due to the electric field. If we look at the interaction with the magnetic field, we find the following features.
`color{blue} {(i)}` It depends on `q, v` and `B` (charge of the particle, the velocity and the magnetic field). Force on a negative charge is opposite to that on a positive charge.
`color{blue} {(ii)}` The magnetic force `q [ v × B ]` includes a vector product of velocity and magnetic field. The vector product makes the force due to magnetic field vanish (become zero) if velocity and magnetic field are parallel or anti-parallel. The force acts in a (sideways) direction perpendicular to both the velocity and the magnetic field. Its direction is given by the screw rule or right hand rule for vector (or cross) product as illustrated in Fig. 4.2.
`color{blue} ✍️{ (iii)}` The magnetic force is zero if charge is not moving (as then `|v|= 0`). Only a moving charge feels the magnetic force. The expression for the magnetic force helps us to define the unit of the magnetic field, if one takes `q, F` and `v`, all to be unity in the force equation
`color{navy}(F = q [ v × B] =q v B sin θ hat n)`
`color {blue}➢` where `θ` is the angle between `v` and `B` [see Fig. 4.2 (a)].
`color{blue} ✍️` The magnitude of magnetic field B is `1 SI` unit, when the force acting on a unit charge `(1 C)`, moving perpendicular to `B` with a speed `1m//s,` is one newton.
Dimensionally, we have `[B] = [F//qv]` and the unit of `B` are Newton second / (coulomb metre).
`color{blue} ✍️` This unit is called tesla (`T`) named after Nikola Tesla (1856 – 1943). Tesla is a rather large unit. A smaller unit (non-SI) called gauss (=`10^(–4)` tesla) is also often used. The earth’s magnetic field is about `(3.6 × 10^(–5) T.)`
`color{blue} ✍️` Table 4.1 lists magnetic fields over a wide range in the universe.
`color{blue} ✍️` Let us suppose that there is a point charge `q` (moving with a velocity `v` and, located at `r` at a given time `t` ) in presence of both the electric field `E (r)` and the magnetic field `B (r)`. The force on an electric charge q due to both of them can be written as
`color{navy}(F = q [ E (r) + v × B (r)] ≡ F_("electric") +F_("magnetic")).........(4.3)`
`color{blue} ✍️` This force was given first by H.A. Lorentz based on the extensive experiments of Ampere and others. It is called the Lorentz force.
`color{blue} ✍️` You have already studied in detail the force due to the electric field. If we look at the interaction with the magnetic field, we find the following features.
`color{blue} {(i)}` It depends on `q, v` and `B` (charge of the particle, the velocity and the magnetic field). Force on a negative charge is opposite to that on a positive charge.
`color{blue} {(ii)}` The magnetic force `q [ v × B ]` includes a vector product of velocity and magnetic field. The vector product makes the force due to magnetic field vanish (become zero) if velocity and magnetic field are parallel or anti-parallel. The force acts in a (sideways) direction perpendicular to both the velocity and the magnetic field. Its direction is given by the screw rule or right hand rule for vector (or cross) product as illustrated in Fig. 4.2.
`color{blue} ✍️{ (iii)}` The magnetic force is zero if charge is not moving (as then `|v|= 0`). Only a moving charge feels the magnetic force. The expression for the magnetic force helps us to define the unit of the magnetic field, if one takes `q, F` and `v`, all to be unity in the force equation
`color{navy}(F = q [ v × B] =q v B sin θ hat n)`
`color {blue}➢` where `θ` is the angle between `v` and `B` [see Fig. 4.2 (a)].
`color{blue} ✍️` The magnitude of magnetic field B is `1 SI` unit, when the force acting on a unit charge `(1 C)`, moving perpendicular to `B` with a speed `1m//s,` is one newton.
Dimensionally, we have `[B] = [F//qv]` and the unit of `B` are Newton second / (coulomb metre).
`color{blue} ✍️` This unit is called tesla (`T`) named after Nikola Tesla (1856 – 1943). Tesla is a rather large unit. A smaller unit (non-SI) called gauss (=`10^(–4)` tesla) is also often used. The earth’s magnetic field is about `(3.6 × 10^(–5) T.)`
`color{blue} ✍️` Table 4.1 lists magnetic fields over a wide range in the universe.