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. $5.17\times 10^{-3}~\text T$