Chapter 24.1, Problem 5PP

(a)

To determine

Strength of the field 2 cm from the wire.

Answer to Problem 5PP

The magnetic field at 1 cm is two times stronger than at 2 cm.

Explanation of Solution

Given:

Magnetic field strength = $1\text{ cm}$

Formula used:

  $B=\frac{{\mu }_{\text{o}}I}{2\pi r}$

Where, B = magnetic field strength

r = distance

Calculation:

As it is clear from the formula that strength of magnetic field is inversely proportional to the distance.

  $B\propto \frac{1}{r}$

So, magnetic field strength will be half when the distance is 2 cm

Conclusion:

The magnetic field at 1 cm is two times stronger than at 2 cm.

(b)

To determine

Strength of the field 3 cm from the wire.

Answer to Problem 5PP

The magnetic field at 1 cm is three times stronger than that at 3 cm.

Explanation of Solution

Given:

Magnetic field strength = $1\text{ cm}$

Formula used:

  $B=\frac{{\mu }_{\text{o}}I}{2\pi r}$

Where, B = magnetic field strength

r = distance

Calculation:

As it is clear from the formula that strength of magnetic field is inversely proportional to the distance.

  $B\propto \frac{1}{r}$

So, magnetic field strength will be three times less when the distance is 3 cm

Conclusion:

The magnetic field at 1 cm is three times stronger than that at 3 cm.