## A magnetic material of volume 30cm³ is placed in a magnetic field of intensity 5 oersted. The magnetic moment produced…..

Q. A magnetic material of volume 30 cm³ is placed in a magnetic field of intensity 5 oersted. The magnetic moment produced due it is 6 amp – m². The value of magnetic induction will be.

(a) 0.2517 Tesla

(b) 0.025 Tesla

(c) 0.0025 Tesla

(d) 25 Tesla

Ans: (a)

Sol: $\displaystyle H = \frac{5\times 10^3}{4 \pi} A/m$

H = 398 A/m

$\displaystyle I = \frac{M}{V}$

$\displaystyle I = \frac{ 6}{30 \times 10^{-6}}$

I = 0.2 × 106

$\displaystyle B = \mu_0 (H + I)$

$\displaystyle B = 4 \pi \times 10^{-7} (398 + 2 \times 10^5)$

B = 0.2517 T

## A rod of ferromagnetic material with dimensions 10cm×5cm× 2cm is placed in a magnetising field of intensity 2 × 10^-5 A/m…..

Q. A rod of ferromagnetic material with dimensions 10 cm × 5 cm × 2 cm is placed in a magnetising field of intensity 2 × 10-5 A/m. The magnetic moment produced due it is 6 amp – m². The value of magnetic induction will be …….10-2T.

(a) 100.48

(b) 200.28

(c) 50.24

(d) 300.48

Ans:(a)

Sol: V = 100 × 10-6 m3

H = 2 × 10-5 A/m

M = 6 amp – m²

$\displaystyle I = \frac{M}{V}$

$\displaystyle B = \mu_0 (H + I)$

## Find the percentage increase in the magnetic field B when the space within the current carrying toroid is filled with aluminum….

Q. Find the percentage increase in the magnetic field B when the space within the current carrying toroid is filled with aluminum. The susceptibility of aluminium is 2.1 × 10-5

(a) 3.1 × 10-3

(b) 1.1 × 10-3

(c) 2.1 × 10-3

(d) 2.1 × 10-5

Ans: (c)

$\displaystyle B_0 = \mu_0 H$ (Where H = n i)

$\displaystyle B = \mu_0 \mu_r H$

$\displaystyle B = \mu_0 (1 + \chi_m) H$

Percentage increase in magnetic field is

$\displaystyle = \frac{B – B_0}{B_0}\times 100$

$\displaystyle = \frac{\mu_0 \chi_m H}{\mu_0 H }\times 100$

$\displaystyle = \chi_m \times 100$

$\displaystyle = 2.1 \times 10^{-5}\times 100$

= 2.1 × 10-3

## 300 turns of a thin wire are uniformly wound on a permanent magnet shaped as a cylinder of length 15cm….

Q. 300 turns of a thin wire are uniformly wound on a permanent magnet shaped as a cylinder of length 15cm. When a current 3A is passed through the wire, the field outside the magnet disappears. Then the coercive force of the material is

(a) 2 kAm-1

(b) 4 kAm-1

(c) 5 kAm-1

(d) 6 kAm-1

Ans : (d)

Sol: coercive force of the material $\displaystyle H = n i = \frac{N}{l}\times i$

$\displaystyle H = \frac{300}{0.15}\times 3$

= 6000 A/m

= 6 kA/m

## What will be the energy loss per hour in the iron core of a transformer if the area of its hysteresis loop is equivalent to 2500erg/cm³….

Q. What will be the energy loss per hour in the iron core of a transformer if the area of its hysteresis loop is equivalent to 2500 erg/cm³. The frequency of alternating current is 50 Hz. The mass of core is 10 Kg and the density of iron is 7.5 gm/cm³.

(a) 2 × 10-2 Joule

(b) 4 × 103 Joule

(c) 6 × 104 Joule

(d) 8 × 105 Joule

Ans: (c)

Sol: Total energy loss

$\displaystyle = \nu A V t$

$\displaystyle = \nu A \times \frac{m}{\rho}\times t$

$\displaystyle = 50 \times \frac{250 \times 10^{-7}}{10^{-6}} \times \frac{10}{7.5 \times 10^3}\times 3600$