Question

Two parallel long current carrying wire separated by a distance $2r$ are shown in the figure. The ratio of magnetic field at $A$ to the magnetic field produced at $C$ is $\frac{x}{7}$. The value of $x$ is ___.

Answer 1

Correct Answer: 5

The magnetic field at point \( A \), \( B_A \), is given by:
\[ B_A = \frac{\mu_0 I}{2 \pi r} + \frac{\mu_0 (2I)}{2 \pi (3r)} = \frac{5 \mu_0 I}{6 \pi r}. \] 
The magnetic field at point \( C \), \( B_C \), is given by: 
\[ B_C = \frac{\mu_0 (2I)}{2 \pi r} + \frac{\mu_0 I}{2 \pi (3r)} = \frac{7 \mu_0 I}{6 \pi r}. \] 
The ratio of magnetic fields \( B_A \) to \( B_C \) is: 
\[ \frac{B_A}{B_C} = \frac{5}{7}. \] 
Thus, we find: 
\[ x = 5. \]