Chapter 24, Problem 73A

a.

To determine

Magnitude and direction of force.

Answer to Problem 73A

  $F\text{=1}\text{.125}\times {\text{10}}^{-2}\text{N/m}$ downward

Explanation of Solution

Given:

Current through the wire, $I=225\text{A}$ towards west

Strength of earth’s magnetic field, $B_{\text{earth}}=5\times {10}^{-5}\text{T}$ towards south

Formula Used:

Force on current carrying wire in magnetic field is given as,

  $F=BIL\sin \theta$

Where, $B$ is strength of magnetic field, $I$ is current through the wire, $L$ is length of wire and $\theta$ is angle of wire with magnetic field.

Calculation:

Angle of wire with magnetic field, $\theta =90°$

On substituting the given values in above relation,

  $\begin{array}{l}F=5\times {10}^{-5}\times 225\times L\times \sin {90}^o\\ \Rightarrow \frac{F}{L}=5\times {10}^{-5}\times 225\text{N/m}\\ \text{=1}\text{.125}\times {\text{10}}^{-2}\text{N/m}\end{array}$

From Flemings Left Hand Rule

As direction of current is towards west (represented by middle finger) and direction of magnetic field is towards south (represented by index finger) so, the direction of force is downward (represented by thumb).

Conclusion:

Therefore, magnitude of force is $F\text{=1}\text{.125}\times {\text{10}}^{-2}\text{N/m}$ and the direction is downward.

b.

To determine

To identify: Whether the magnetic force obtained in part (a) is important in designing the tower or not.

Answer to Problem 73A

No, the magnetic force obtained in part (a) is not important in designing the tower or not.

Explanation of Solution

Given:

Current through the wire, $I=225\text{A}$ towards west

Strength of earth’s magnetic field, $B_{\text{earth}}=5\times {10}^{-5}\text{T}$ towards south

For a transmission line wire the general weight is around 3 N/m to 5 N/m

The above calculated magnetic force is $F=\text{0}\text{.01125}\text{N/m}$

Since the magnetic force $F=\text{0}\text{.01125}\text{N/m}$ is very small as compared to the weight of the wire which is around 3 N/m to 5 N/m.

So, the magnetic force can be neglected in comparison of weight of wire.

Hence it is not important in designing of towers.