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Chapter 4: Q38E (page 950)

A closely wound coil has a radius of 6.00 cm and carries a current of 2.50 A. How many turns must it have if, at a point on the coil axis 6.00 cm from the centre of the coil, the magnetic field is6.39脳10-4T.

Short Answer

Expert verified

The number of turns is 69.

Step by step solution

01

Concept of the magnetic field

The magnetic field due to a loop of radius a at any point x on the axis of loop is given by:

Bx=渭0Nla22x2+a23/2

Where N is the number of turns, and I is the current passing through the loop.

02

Calculate the number of terms

Consider a closely wound coil that has a radius of, and it carries a current ofWe need to find the number of turns such that the magnetic field is BCat a point on the coil axis 6.00 cm from the center of the coil.

To calculate N, we have:

N=2Bxx2+a23/2渭0a2

Substitute the values, and we get;

role="math" localid="1668249432744" N=26.39脳10鈭�4T(0.0600m)2+(0.0600m)23/24蟺脳10鈭�7T鈰�m/A(2.50A)(0.0600m)2=69

Therefore, the number of turns is 69.

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