Question

Using the formula →F =q→v ×→B and B=μ0i2πr, show that the SI units of the magnetic field B and the permeability constant µ0 may be written as N mA−1 and NA−2 respectively.

Answer 1

Explanation:

Step 1:

According to Lorentz Force relation :

We know that  

$\vec{F}=\overrightarrow{q v} \times \vec{B}$

we get

$B=\frac{F}{q v}=\frac{F}{(1 t v)}$

Units of

Force (F) = N

Current (I) = A

Time (T) = s

Velocity (v) = m/s

Step 2: Magnetic field B

B=N/(A-m)  

Now,

The wire is encircled by the magnetic field created by a steady current flowing through a very long straight line. It has magnitude at a point P a radial distance from the wire

$B=\frac{N}{A-m}$

Step 3: Permeability constant

Rearrange the above equation, we get  

 $\mu_{0}=B \frac{2 \pi r}{i}=\frac{N}{A-m} \times \frac{m}{A}$

$\mu_{0}=\frac{N}{A^{2}}$

Hence proved