Question

When a plate of magnetic material of size 10 cm × 0.5 cm × 0.2 cm (length, breadth, and thickness respectively ) is located in the magnetizing field of 0.5 × 10⁴ Am^-1 then a magnetic moment of 5 Am² is induced in it. Find out magnetic induction in the plate.   

Answer 1

Given:

l = 10 cm = 10^-1 m,
b = 0.5 cm = 5 × 10^-3 m,
h = 0.2 cm = 2 × 10^-3 m,
H = 0.5 × 10⁴ Am^-1 =  5 × 10³ Am^-1 
μ₀ = 4π × 10^-7 TmA^-1
m_net = 5 Am² 

To find: Magnetic induction in the plate (B)

Formulae:

1. M = `"m"_"net"/"V"`
2. B = μ₀ = (M + H)

Calculation: 

From formula (i),

M = `5/(10^-1 xx 5 xx 10^-3 xx 2 xx 10^-3)`

= 5 × 10⁶ Am^-1

From formula (ii),

B = `4 xx 3.142 xx 10^-7 [5 xx 10^6 + 5 xx 10^3]`

= `12.568 xx 10^-7 xx 5 xx 10^3 [10^3 + 1]`

= `6.284 xx 10^-3 xx 1001`

= `6.29 xx 10^3 xx 10^-3`

= 6.29 T

Magnetic induction in the plate is 6.29 T.