The radius of the path of an electron and frequency (mass $9\times {10}^{-31} \mathrm{kg}$ and charge $1.6\times {10}^{-19} \mathrm{C}$) moving at a speed of \(3\times10^7\) m/s in a magnetic field of \(6\times10^{-4}\) T perpendicular to it are respectively:
1. \(24\) cm, \(4\) MHz
2. \(22\) cm, \(4\) MHz
3. \(28\) cm, \(2\) MHz
4. \(26\) cm, \(2\) MHz

An electron $\left(mass 9\times {10}^{-31} kg and charge 1.6\times {10}^{-19} C\right)$ is moving at a speed of 3 ×10⁷ m/s in a magnetic field perpendicular to it. The energy of the electron in keV is: ( 1 eV = 1.6 × 10^–19 J)

1. 2.5 keV

2. 3.5 keV

3. 20 keV

4. 3.0 keV

An element \(\Delta l=\Delta x \hat{i}\) is placed at the origin and carries a large current of \(I=10\) A (as shown in the figure). What is the magnetic field on the \(y\text-\)axis at a distance of \(0.5\) m? (\(\Delta x=1~\text{cm}\))
       

         
1. \(0\)
2. \(1.2\times 10^{-4}~\text{T}\)
3. \(2.1\times 10^{-4}~\text{T}\)
4. None of these

A straight wire carrying a current of 12 A is bent into a semi-circular arc of radius 2.0 cm as shown in the figure. Consider the magnetic field B at the centre of the arc. What is the magnetic field at centre due to the semi-circular loop?

$1. 0$
$2. 3.8\times {10}^{-4} T$
$3. 1.9\times {10}^{-4} T$
$4. 2.9\times {10}^{-4} T$

Consider a tightly wound \(100\) turn coil of radius \(10\) cm, carrying a current of \(1\) A. What is the magnitude of the magnetic field at the centre of the coil?
1. \(8.2\times10^{-4}\) T
2. \(4.6\times10^{-4}\) T
3. \(5.2\times10^{-4}\) T
4. \(6.2\times10^{-4}\) T

The figure shows a long straight wire of a circular cross-section (radius a) carrying steady current I. The current I is uniformly distributed across this cross-section. If the magnetic field in the region (r < a) is $B_1$ and for (r > a) is $B_2$, then $\frac{B_1}{B_2}$ is:

$1. \frac{a}{r}$
$2. \frac{a^2}{r^2}$
$3. \frac{r^2}{a^2}$
$4. \frac{r}{a}$

A solenoid of length 0.5 m has a radius of 1 cm and is made up of 500 turns. It carries a current of 5 A. What is the magnitude of the magnetic field inside the solenoid?

$1. 6.28\times {10}^{-3} T$
$2. 3.14\times {10}^{-3} T$
$3. 2.72\times {10}^{-3} T$
$4. 5.17\times {10}^{-3} T$

The horizontal component of the earth’s magnetic field at a certain place is \(3.0\times10^{-5}~\text{T}\) and the direction of the field is from the geographic south to the geographic north. A very long straight conductor is carrying a steady current of \(1~\text{A}\). What is the force per unit length on it when it is placed on a horizontal table and the direction of the current east to west?
1. \(3\times10^{-5}~\text{N m}^{-1}\)
2. \(2\times10^{-7}~\text{N m}^{-1}\)
3. zero
4. \(5\times10^{-7}~\text{N m}^{-1}\)

The horizontal component of the earth’s magnetic field at a certain place is 3.0 ×10^–5 T and the direction of the field is from the geographic south to the geographic north. A very long straight conductor is carrying a steady current of 1 A. What is the force per unit length on it when it is placed on a horizontal table and the direction of the current is south to north?

$1. 3\times {10}^{-5} N m^{-1}$
$2. 2\times {10}^{-7} N m^{-1}$
$3. 0$
$4. 5\times {10}^{-7} N m^{-1}$