Compare the magnitude of the magnetic field at the center of a circular current loop of radius 20 mm with the magnitude of the magnetic field at the center of a solenoid of the same radius and with 2.0 turn per millimeter. Assume the current is the same through the current loop and the solenoid.

The magnitude of the magnetic field at the center of a solenoid is 80 times of the magnetic field at the center of a loop.

Explanation:

Given that,

Radius = 20 mm

Number of turns = 2000

Suppose, we can use wire of 1.0 mm diameter to make either a single loop of wire or a solenoid, and we wish to compare, for a given current, the magnetic fields at the center of each.

Suppose a small element of wire of length dl.

Let I be the current flowing through the wire

We need to calculate the magnetic field

Using formula of magnetic field

Put the value into the formula

...(I)

We need to calculate the magnetic field due to solenoid

Using formula of magnetic field

...(II)

We need to calculate the magnitude of the magnetic field at the center of a circular current loop

Dividing equation (II) by equation (I)

Put the value into the formula

Hence, The magnitude of the magnetic field at the center of a solenoid is 80 times of the magnetic field at the center of a loop.

explanation:

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