A straight wire of mass \(200~\text{g}\) and length \(1.5~\text{m}\) carries a current of \(2~\text{A}\). It is suspended in mid-air by a uniform horizontal magnetic field \(B\) (shown in the figure). What is the magnitude of the magnetic field?

In a region of space, magnetic field is parallel to the positive \(y\text-\)axis and the charged particle is moving along the positive \(x\text-\)axis (as shown in the figure). The directions of Lorentz force for an electron (negative charge) and proton (positive charge) are respectively:

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 \(I=10~\text A\) (as shown in the figure). What is the magnetic field on the \(y\text-\)axis at a distance of \(0.5~\text m?\) 
\((\text{Given}~\Delta x=1~\text{cm})\)

A straight wire carrying a current of \(12~\text A\) is bent into a semi-circular arc of radius \(2.0 ~\text{cm}\) 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. Zero
2. \( 3 . 8 \times10^{- 4}  ~\text T\)
3. \(1.9\times10^{- 4}  ~\text T\)
4. \(2.9 \times10^{- 4}  ~\text T\)$$

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?

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 \(0.5~\text m\) has a radius of \(1~\text{cm}\) and is made up of \(500\) turns. It carries a current of \(5~\text A.\) What is the magnitude of the magnetic field inside the solenoid?
1. \(6.28\times 10^{-3}~\text T\)
2. \(3.14\times 10^{-3}~\text T\)
3. \(2.72\times 10^{-3}~\text T\)
4. \(5.17\times 10^{-3}~\text T\)