Question

A circular coil carrying a current I has radius R and number of turns N . If all three, i.e the current I, radius R and number of turns N are doubled, then magnetic field at its center becomes:

• A. Double
• B. Half
• C. Four times
• D. One-fourth

Answer 1

The correct option is A Double

Concept

Magnetic field at the centre of coil is given by,

B= $\frac{UNI}{2R}$

Solution:

New current, I' = 2I

New radius, R' = 2R

New number of turns , N' = 2N

Therefore, New Magnetic Field,B' =$\frac{U\times 2N\times 2I}{2\times 2R}$

$\Rightarrow B^{\prime }=2\times \frac{UNI}{2R}$

$\Rightarrow B^{\prime }=2\times B$

Hence, option A is correct.