Question

The magnetic field inside a current carrying toroidal solenoid is B, if its radius is doubled and the current through it is also doubled keeping the total number of turns same, the magnetic field inside the solenoid will be:

• A. B/2
• B. B
• C. 2B
• D. 4B

Answer 1

The correct option is B B

Given :

The magnetic field inside a current carrying toroidal solenoid is B,

the radius and the current throught it are doubled keeping the no. of turns same.

Solution :

Let the radius is r and current through it is I

According to Ampere's Circuital law,

$B=\frac{\mu 0\ast N\ast I}{2\pi \ast r}$

But according to the question, new radius r0=2r

the new passing current I0=2I

Hence,

$B0=\frac{\mu 0\ast N\ast 2I0}{2\pi \ast 2r0}$

$B0=\frac{\mu 0\ast N\ast 2I}{2\pi \ast 2r}$

$B0=B$

The correct answer is : B