Two protons move parallel to each other, keeping distance $r$ between them, both moving with same velocity $\vec V\,$. Then the ratio of the electric and magnetic force of interaction between them is
Advanced
Download our app for free and get started
Electric force $\mathrm{Fe}=\mathrm{kq}_{1} \mathrm{q}_{2} / \mathrm{r}^{2}=\mathrm{kq}^{2} / \mathrm{r}^{2}$
Magnetic force $=\mathrm{qv}\left(\frac{\mu_{0}}{4 \pi} \times \frac{\mathrm{qv}}{r^{2}}\right)$
$\mathrm{F}_{\mathrm{m}}=\mathrm{q}^{2} \mathrm{v}^{2}\left(\frac{\mu_{0}}{4 \pi}\right) \frac{1}{\mathrm{r}^{2}}$
$\frac{F e}{F_{m}}=\frac{k}{v^{2}\left(\frac{\mu_{0}}{4 \pi}\right)}=\frac{1}{v^{2} \varepsilon_{0} \mu_{0}}=\frac{c^{2}}{v^{2}}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Electron moves at right angles to a magnetic field of $1.5 \times 10^{-2}\,tesla$ with speed of $6 \times 10^7\,m/s$. If the specific charge of the electron is $1.7 \times 10^{11}\,C/kg$. The radius of circular path will be......$cm$View Solution
- 2A long solenoid of $50\, cm$ length having $100$ turns carries a current of $2.5$ $A.$ The magnetic field at the centre of the solenold is $...... \times 10^{-5}\;T$View Solution
$\left(\mu_{0}=4 \pi \times 10^{-7}\, T\, m\, A ^{-1}\right)$
- 3If a proton enters perpendicularly a magnetic field with velocity $v$, then time period of revolution is $T$. If proton enters with velocity $2 v$, then time period will beView Solution
- 4In the adjoining circuit diagram, the readings of ammeter and voltmeter are $2\, A$ and $120 \,V$, respectively. If the value of $R$ is $75\, \Omega$, then the voltmeter resistance will be $\Omega$View Solution
- 5Match List $I$ with List $II$View Solution
Choose the correct answer from the options given below:
- 6The magnetic field is uniform for $y>0$ and points into the plane. The magnetic field is uniform and points out of the plane for $y<0$. A proton denoted by filled circle leaves $y=0$ in the $-y$-direction with some speed as shown below.Which of the following best denotes the trajectory of the proton?View Solution
- 7Two infinite length wires are placed according to figure. Magnitude of magnetic field at point $M$ which is mid point of line joining the two wireView Solution
- 8View SolutionIdentical currents flow in two perpendicular wires, as shown in the figure. The wires are very close but do not touch. The magnetic field can be zero:
- 9A galvanometer having coil resistance $10 \ \Omega$ shows a full scale deflection for a current of $3 \mathrm{~mA}$. For it to measure a current of $8 \mathrm{~A}$, the value of the shunt should be:View Solution
- 10A circular coil of $30$ turns and radius $8.0\, cm$ carrying a current of $6.0\, A$ is suspended vertically in a uniform horizontal magnetic field of magnitude $1.0\, T$. The field lines make an angle of $60^o$ with the normal of the coil. Calculate the magnitude of the counter torque that must be applied to prevent the coil from turning.....$Nm$View Solution