Question

The medical diagnostic technique called magnetic resonance imaging (MRI) requires that patient lie in a strong magnetic field. It consists of two large solenoids, placed above and below.

1. What is solenoid?

2. Which law help you to find magnetic field due to solenoid? State the law.

3. Obtain an expression for magnetic field due to solenoid using the above law.

4. If the diameter of one of the MRI coil is increased without changing the current, does the magnetic field that it produce at its centre increases, decreases or stay the same? Justify.

Answer 1

1. An insulated conducting wire wound in the form of cylinder is called solenoid.

2. Ampere’s circuital law:

Ampere’s circuital theorem states that the line integral of the magnetic field around any closed path in free space is equal to µ₀ times the net current passing through the surface.

3. 

Consider a solenoid having radius Y. Let ‘n’ be the number of turns per unit length and I be the current owing through it.

In order to find the magnetic field (inside the solenoid) consider an Amperian loop PQRS. Let ‘l‘ be the length and ‘b’ the breadth

Applying Amperes law, we can write

(Since RS is completely out side the solenoid, for which B = 0)

Substituting the above values in eq (1), we get

Bl = µ₀l_enc (2)

But I_enc = n II

where ’nI ’ is the total number of turns that carries current I (inside the loop PQRS)

∴ eq (2) can be written as

Bl = µ₀ nII

B = µ₀ nI

If core of solenoid is filled with a medium of relative permittivity µ_r , then

B = µ₀ µ_r nI

4. No change. Magnetic field is independent of radius.