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Question7. Power lines 12 m from the ground carry 4.50×103 A4.50 \times 10^{3} \mathrm{~A} of current across a farmer's field. What magnetic field strength do the cattle directly underneath experience? ( 3 marks)

Studdy Solution

STEP 1

1. The power lines are considered as long, straight conductors.
2. The current flowing through the power lines is 4.50×103 A 4.50 \times 10^3 \, \text{A} .
3. The distance from the power lines to the cattle is 12 m 12 \, \text{m} .
4. The magnetic field is calculated using the Biot-Savart Law for a long straight conductor.

STEP 2

1. Recall the formula for the magnetic field around a long straight conductor.
2. Substitute the given values into the formula.
3. Calculate the magnetic field strength.

STEP 3

Recall the formula for the magnetic field B B around a long straight conductor carrying current I I at a distance r r :
B=μ0I2πr B = \frac{\mu_0 I}{2 \pi r}
where μ0=4π×10−7 T⋅m/A \mu_0 = 4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A} is the permeability of free space.

STEP 4

Substitute the given values into the formula:
B=(4π×10−7 T⋅m/A)×(4.50×103 A)2π×12 m B = \frac{(4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A}) \times (4.50 \times 10^3 \, \text{A})}{2 \pi \times 12 \, \text{m}}

STEP 5

Calculate the magnetic field strength:
B=(4π×10−7)×(4.50×103)2π×12 B = \frac{(4\pi \times 10^{-7}) \times (4.50 \times 10^3)}{2 \pi \times 12}
Simplify the expression:
B=4×10−7×4.50×1032×12 B = \frac{4 \times 10^{-7} \times 4.50 \times 10^3}{2 \times 12}
B=18×10−424 B = \frac{18 \times 10^{-4}}{24}
B=0.75×10−4 B = 0.75 \times 10^{-4}
B=7.5×10−5 T B = 7.5 \times 10^{-5} \, \text{T}
The magnetic field strength experienced by the cattle is:
7.5×10−5 T \boxed{7.5 \times 10^{-5} \, \text{T}}

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