A long straight cable contains 7 strands of wire each carrying a current of 5 A. The magnetic induction at a distance of 2 cm from the axis of the cable is

Options

A. `5 xx 10^(-5)` T
B. `3.5 xx 10^(-4)` T
C. `3.5 xx 10^(-4)` T
D. `1.1 xx 10^(-3)` T

Explanation

To find the magnetic induction (magnetic field) at a distance of 2 cm from a long straight cable containing 7 strands of wire, each carrying a current of 5 A, we can use the formula for the magnetic field around a long straight conductor:

### Step-by-Step Solution:

1. **Identify the Parameters**:
- Number of strands (n) = 7
- Current in each strand (I) = 5 A
- Distance from the wire (r) = 2 cm = 0.02 m
- Permeability of free space (μ₀) = 4π × 10⁻⁷ T·m/A

2. **Calculate the Total Current**:
Since there are 7 strands, the total current (I_total) flowing through the cable is:
\[ I_{\text{total}} = n \times I = 7 \times 5 \, \text{A} = 35 \, \text{A} \]

3. **Use the Formula for Magnetic Field**:
The magnetic field (B) at a distance r from a long straight wire carrying current I is given by:
\[ B = \frac{\mu_0 I}{2 \pi r} \]
Substitute μ₀ and the total current into the formula:
\[ B = \frac{4\pi \times 10^{-7} \, \text{T·m/A} \times 35 \, \text{A}}{2 \pi \times 0.02 \, \text{m}} \]

4. **Simplify the Equation**:
The π terms cancel out:
\[ B = \frac{4 \times 10^{-7} \times 35}{2 \times 0.02} \]

5. **Calculate the Magnetic Field**:
\[ B = \frac{140 \times 10^{-7}}{0.04} = 3.5 \times 10^{-6} \, \text{T} \]

6. **Convert to Tesla**:
The magnetic field can be expressed in microtesla (µT):
\[ B = 35 \, \mu T \]

### Final Answer:
The magnetic induction at a distance of 2 cm from the axis of the cable is **3.5 × 10⁻⁶ T** or **35 µT**.