Question

A coil of two turns is made of a wire length L and another coil of four turns is made from same length L. When the same current is flowing in two coils, then the ratio of magnetic inductions at their centres is:

• A. \(8:1\)
• B. \(1:4\)
• C. \(9:1\)
• D. \(2:7\)

Hint:

The magnetic field inside a coil is stronger with more turns, assuming all other factors are constant.

Answer 1

The Correct Option is B

Step 1: Understand the relationship between turns and magnetic induction. Magnetic induction \( B \) is directly proportional to the number of turns \( N \) and inversely proportional to the area \( A \), assuming the current \( I \) is the same. \[ B \propto \frac{N}{A} \] Step 2: Calculate the ratio. For the first coil with two turns: \[ B_1 \propto \frac{2}{A_1} \] For the second coil with four turns: \[ B_2 \propto \frac{4}{A_2} \] Given that the wire length and hence the total area is the same, \[ \frac{B_1}{B_2} = \frac{2}{4} = 1:4 \]