Two identical bar magnets with a length of $10 \, cm$ and a weight of $50 \, g$ are placed freely with their like poles facing each other in an inverted vertical glass tube. The upper magnet hangs in the air above the lower one such that the distance between the nearest poles of the magnets is $3 \, mm$. The pole strength of each magnet is approximately ....... $A \cdot m$.

Two short bar magnets of length $1 \ cm$ each have magnetic moments $1.20 \ Am^2$ and $1.00 \ Am^2$ respectively. They are placed on a horizontal table parallel to each other with their $N$ poles pointing towards the South. They have a common magnetic equator and are separated by a distance of $20.0 \ cm$. The value of the resultant horizontal magnetic induction at the mid-point $O$ of the line joining their centres is close to (Horizontal component of Earth's magnetic induction is $3.6 \times 10^{-5} \ Wb/m^2$)

Two short magnets of magnetic moment $1000 \, A m^2$ are placed as shown at the corners of a square of side $10 \, cm$. The net magnetic induction at $P$ is....$T$

Match the items in List-$I$ with the items in List-$II$:
| List-$I$ | List-$II$ |
| :--- | :--- |
| $(A)$ High retentivity | $(i)$ Telephone diaphragm |
| $(B)$ High resistivity | (ii) Diamagnet |
| $(C)$ Low coercivity | (iii) To decrease eddy current losses |
| $(D)$ Negative susceptibility | (iv) Permanent magnet |

Match List-$I$ with List-$II$.

List-$I$	List-$II$
$(a)$ Magnetic Induction	$(i)$ ${ML}^{2} {T}^{-2} {A}^{-1}$
$(b)$ Magnetic Flux	$(ii)$ ${M}^{0} {L}^{-1} {A}$
$(c)$ Magnetic Permeability	$(iii)$ ${MT}^{-2} {A}^{-1}$
$(d)$ Magnetization	$(iv)$ ${MLT}^{-2} {A}^{-2}$

Choose the most appropriate answer from the options given below:

$A$ bar magnet has a total length $2l = 20$ units and the field point $P$ is at a distance $d = 10$ units from the centre of the magnet. If the relative uncertainty of length measurement is $1\%$,then the uncertainty of the magnetic field at point $P$ is