Question

In the cyclotron, as radius of the circular path of the charged particle increases, (\(ω\) = angular velocity, V = linear velocity)

• A. V increases , \(ω\) decreases.
• B. V increases , \(ω\) remains constant.
• C. only \(ω\) increases , V remains constant.
• D. both \(ω\) and V increase.

Hint:

The wire length is fixed, so n turns have radius R over n.

Answer 1

The Correct Option is B

Step 1: Scaling argument:
Field of a coil $\propto\frac{N}{r}$.

Step 2: Apply:
Going from one turn to n turns multiplies N by n and divides r by n, so $\frac Nr$ grows by $n\times n = n^2$. Ratio single : n-turn $= 1 : n^2$ (C).

Final Answer:
$1 : n^2$. \[ \boxed{1 : n^2} \]