Question

Verify the units obtained for magnetic field strength B in example (using the equation $B=\frac{E}{c}$are in fact teslas (T).

Short answer

B=T is the SI unit of a magnetic field.

Step-by-step solution

Definition of magnetic field

The area of space near a magnetic body or a current-carrying body where magnetic forces caused by the body or current can be detected.

Find the value of the magnetic field

Relation between the magnetic field (B), electric field (E), and speed of the light (c) are connected

$B=\frac{E}{c}$……………..(1)

Since the Newton per unit ampere meter is also defined as tesla (T). Therefore, we can write,

$T=\frac{N}{A.m}$

If E is the electric field at any place, then the force F that a charge q is subjected to is given by,

$$\begin{gathered} F=qE \\ E=\frac{F}{q} \end{gathered}$$

The net charge q that passes through a cross-section of the wire in time interval t is defined as current I.

$$\begin{gathered} l=\frac{q}{t} \\ q=l\times t \end{gathered}$$

When we change the values of E and q in the equation above, we will get,

$$\begin{gathered} B=\frac{F}{q\times c} \\ =\frac{F}{l\times t\times c} \end{gathered}$$

Now, in the preceding equation, substitute the units of Force, Current, time, and speed:

$$\begin{gathered} B=\frac{N}{A.s.m/s} \\ =\frac{N}{A.m} \end{gathered}$$

Thus,

$$\begin{gathered} B=\frac{N}{A.m} \\ =T \end{gathered}$$

Therefore, B=T is the SI unit of the magnetic field.