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.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Draw a plot of potential energy of a pair of nucleons as a function of their separations. Mark the regions where the nuclear force is (i) attractive and (ii) repulsive. Write any two characteristic features of nuclear forces.
The kinetic energy of a charged particle decreases by 10J as it moves from a point at potential 100V to a point at potential 200V. Find the charge on the particle.
Describe principle and construction of AC generator with figure and discuss its working.
The magnetic field at a point inside a 2.0mH inductor coil becomes 0.80 of its maximum value in 20µs when the inductor is joined to a battery. Find the resistance of the circuit.
Each of the plates shown in figure has surface area $\Big(\frac{96}{\in_0}\Big)\times10^{-12}\text{Fm}$ on one side and the separation between the consecutive plates is 4.0mm. The emf of the battery connected is 10 volts. Find the magnitude of the charge supplied by the battery to each of the plates connected to it.
→Does the force on a charge due to another charge depend on the charges present nearby?
You are given a circuit below. Write its truth table. Hence, identify the logic operation carried out by this circuit. Draw the logic symbol of the gate it corresponds to.
What is the nature of electromagnetic waves?
A charge Q is uniformly distributed over a rod of length l. Consider a hypothetical cube of edge l with the centre of the cube at one end of the rod. Find the minimum possible flux of the electric field through the entire surface of the cube.
Explain principle, construction and working of optical fibre.