Biot-Savart Law - report PDF

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Name: ................................................................................................ ID no: ...............................

Class and Section: ...............................

Practical Course: The Biot-Savart Law I.

Objectives

1. To calculate the magnetic field

of a long coil (Solenoid) as a function of the

current I passing through it. 2. To calculate the magnetic field of a long coil (Solenoid) as a function of its length L and number of its turns N. 3. To calculate the magnetic field on the axis of a circular current loop.

II.

Apparatus: DC power supply, magnetic field sensor, solenoid of different lengths and number of turns, banana plugs wire connections.

III.

Theory

To find the magnetic field

due to a current I passing in a length element

at any point

in the space, we use the Biot-Savart Law, which is given by:

………………………….……… (1) Where, µ o is the permeability of air = 4π × 10-7 T.m/A, I is the passing current,

is a

vector with length dl in the same direction as the current in the conductor and r is the distance from

to the point which the magnetic field needs to be calculated. To calculate

the total magnetic field due to all current elements, we integrate equation 1 over all segments dl that carry current. For a Solenoid of number of turns N and total length L, the magnetic field can be easily found using Ampere's Law. B = µ o N I / L ………………………………..(2) For a circular loop with radius a and carries current I, the magnetic field on its axis is given by:

……………………………............(3) Where, x is the distance from the circular loop center to the point that the magnetic field needs to be calculated, and N is the number of turns of the circular coil. When x = 0 in equation 3, i.e. on its center, equation 3 reads: ………………………………………………….(4) Dr. S. Salman and Dr. A. Abuzir

Name: ................................................................................................ ID no: ...............................

IV.

Class and Section: ...............................

Experimental procedure and data analysis A. The Magnetic Field of a Solenoid

 Adjust the tip of magnetic probe of the magnetic field sensor at the Solenoid axis.  Connect the circuit shown in Figure 1 below.  Fix the magnetic field sensor range at 20 mT, and then calibrate the reading to zero.  Choose a suitable value of the current I and fix it, change the length of the solenoid by gently pulling its end. Record the magnetic field from the magnetic field sensor. Fill in table 1.  Important Note: Calibrate to zero after every reading.

Figure 1

No.

L(m)

B (mT)

Table 1  Fix the solenoid length L, change the value of the current I that passes in the solenoid. Record the magnetic field from the magnetic field sensor for each reading. Fill in table 2.

No.

I(amp)

B (mT)

Table 2 Dr. S. Salman and Dr. A. Abuzir

Name: ................................................................................................ ID no: ...............................

Class and Section: ...............................

 Plot B vs I. calculate the slope and from it find µo

 Calculate the percentage error in µo, Consider the true value of µo = 4π × 10-7 T.m/A

 Plot the relation between B vs L, Does it agree with equation 2?

B. The Magnetic Field of a circular loop  Measure the magnetic field B0 at the center of the circular loops, i.e. x = 0.  Measure the magnetic field B1 away from the center of the circular loops, i.e. x+ (in the positive x-axis direction).  Measure the magnetic field B2 away from the center of the circular loops, i.e. x - (in the negative x-axis direction).  Fill your data in table 3. N = …………………………………., a = ………………………………. (m)

No.

B0 (mT)

B1 (mT)

B2 (mT)

X=0

X+ (m)

X- (m)

Table 3  Plot the relation between B vs x.

Dr. S. Salman and Dr. A. Abuzir...