Question
Explain Lorentz force and state its characteristics.
✓
Answer
→Suppose a point charge $q$ moving with a velocity $\vec{v}$ in presence of the electric field $\overrightarrow{ E }(\vec{r})$ and the magnetic field $\overrightarrow{ B }(\vec{r})$.
→Force on charge $q$ due to the electric and magnetic field.
$\begin{aligned}
\overrightarrow{ F } & =q[\overrightarrow{ E }(r)+(\vec{v} \times \overrightarrow{ B }(\vec{r}))] \\
\therefore \quad \overrightarrow{ F } & =q \overrightarrow{ E }(\vec{r})+q \times \times \overrightarrow{ B })
\end{aligned}$
[Here $\overrightarrow{ B }(r)=\overrightarrow{ B }$ ]
Electric force $\overrightarrow{ F }_{\text {electric }}=q \cdot \overrightarrow{ E }(\vec{r})$
Magnetic force $\overrightarrow{ F }$. magnetic $=q(\overrightarrow{ v } \times \overrightarrow{ B })$
$\therefore \overrightarrow{ F }=\overrightarrow{ F }_{\text {electric }}+\overrightarrow{ F }_{\text {magnetic }}$
→The combination of electric and magnetic force here is known as Lorentz force.
• Characteristics :
(1) The Lorentz force depends on charge ( $q$ ), velocity ( $\vec{v}$ ) and the magnetic field $(\vec{B})$. Force on negative charge is opposite to that on a positive charge.
(2) The direction of magnetic force $\vec{F}_m=q(\vec{v} \times$ $\vec{B}$ ) can be found using right hand screw rule.
(3) If velocity $\vec{v}$ and the magnetic field $\vec{B}$ are parallel $(\theta=0)$ anti parallel $\left(\theta=180^{\circ}, \pi\right)$ to each other, the force becomes zero.
The magnetic force is maximum when the velocity $\vec{v}$ and the magnetic field $\vec{B}$ are perpendicular to each other.
(4) If charge is not moving i.e. the charge is stationary. then $\vec{v}=0$ hence the magnetic force is zero.
→Force on charge $q$ due to the electric and magnetic field.
$\begin{aligned}
\overrightarrow{ F } & =q[\overrightarrow{ E }(r)+(\vec{v} \times \overrightarrow{ B }(\vec{r}))] \\
\therefore \quad \overrightarrow{ F } & =q \overrightarrow{ E }(\vec{r})+q \times \times \overrightarrow{ B })
\end{aligned}$
[Here $\overrightarrow{ B }(r)=\overrightarrow{ B }$ ]
Electric force $\overrightarrow{ F }_{\text {electric }}=q \cdot \overrightarrow{ E }(\vec{r})$
Magnetic force $\overrightarrow{ F }$. magnetic $=q(\overrightarrow{ v } \times \overrightarrow{ B })$
$\therefore \overrightarrow{ F }=\overrightarrow{ F }_{\text {electric }}+\overrightarrow{ F }_{\text {magnetic }}$
→The combination of electric and magnetic force here is known as Lorentz force.
• Characteristics :
(1) The Lorentz force depends on charge ( $q$ ), velocity ( $\vec{v}$ ) and the magnetic field $(\vec{B})$. Force on negative charge is opposite to that on a positive charge.
(2) The direction of magnetic force $\vec{F}_m=q(\vec{v} \times$ $\vec{B}$ ) can be found using right hand screw rule.
(3) If velocity $\vec{v}$ and the magnetic field $\vec{B}$ are parallel $(\theta=0)$ anti parallel $\left(\theta=180^{\circ}, \pi\right)$ to each other, the force becomes zero.
The magnetic force is maximum when the velocity $\vec{v}$ and the magnetic field $\vec{B}$ are perpendicular to each other.
(4) If charge is not moving i.e. the charge is stationary. then $\vec{v}=0$ hence the magnetic force is zero.
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