Field strength factors

Directional Changes and Strength

While the magnitude of the magnetic field strength depends only on the size of the current and the distance, the direction of the field is linked to the direction of the current:

• If the conventional current is reversed, the direction of the magnetic field also reverses.
• However, if the magnitude of the current remains the same, the magnetic field strength at any given distance remains unchanged.

Mathematical Verification of Field Strength

To verify the inversely proportional relationship between field strength and distance from the wire, you can use the "constant product" method. If the relationship is truly inversely proportional, then the product of the two variables must be constant: $\text{Magnetic Flux Density} (B) \times \text{Distance} (r) = \text{Constant}$

Distance from wire ($r$) in $\text{m}$	Flux Density ($B$) in $\text{T}$	Product ($B \times r$)

Because the product remains constant ($0.04$), it confirms that $B$ is inversely proportional to $r$.

Worked Example: Inverse Proportionality

A current flows through a wire. At a distance of $0.05\text{ m}$, the magnetic flux density is $8\text{ T}$. Calculate the magnetic flux density at a distance of $0.20\text{ m}$.

Step 1: Identify the change in distance. The distance has increased from $0.05\text{ m}$ to $0.20\text{ m}$. $0.20 / 0.05 = 4$. The distance has quadrupled ($4 \times r$).

Step 2: Apply the inverse proportionality rule. Because $B \propto 1/r$, quadrupling the distance will reduce the field strength to one-quarter ($\frac{1}{4} \times B$).

Step 3: Calculate the final value. $8\text{ T} \times 0.25 = 2\text{ T}$