Question

The magnetic field at the centre of a circular coil of radius $r$ carrying a current $I$ is proportional to

• A. $I / r$
• B. $I r$
• C. $I / r^2$
• D. $I r^2$

Hint:

Remember that for circular coils, the magnetic field strength decreases as the radius increases, and it directly depends on the current flowing through the coil.

Answer 1

The Correct Option is A

Step 1: Recall the field of a coil.
The magnetic field at the center of a circular coil carrying current $I$ is \[ B = \frac{\mu_0 I}{2r} \] where $\mu_0$ is a constant and $r$ is the radius.

Step 2: Spot the current term.
The current $I$ is on top, so the field grows with the current. \[ B \propto I \] More current makes a stronger field.

Step 3: Spot the radius term.
The radius $r$ is on the bottom to the first power, so the field falls as the coil gets bigger. \[ B \propto \frac{1}{r} \]

Step 4: Combine the two.
Putting both together, \[ B \propto \frac{I}{r} \]

Step 5: Rule out the others.
Forms with $r^2$ or $Ir$ do not match the simple $I/r$ behavior given by the formula.

Step 6: State the answer.
The field at the center is proportional to current divided by radius. \[ \boxed{B \propto \frac{I}{r}} \]