Question

A solenoid that is 35 cm long and contains 450 circular coils 2.0 cm in diameter carries a 1.75-A current. (a) What is the magnetic field at the center of the solenoid, 1.0 cm from the coils? (b) Suppose we now stretch out the coils to make a very long wire carrying the same current as before. What is the magnetic field 1.0 cm from the wire’s center? Is it the same as that in part (a)? Why or why not?

Answer 1

Answer:

Explanation:

a )  No of turns per metre

n = 450 / .35

= 1285.71

Magnetic field inside the solenoid

B = μ₀ n I

Where I is current

B = 4π x 10⁻⁷ x 1285.71 x 1.75

= 28.26 x 10⁻⁴ T

This is the uniform magnetic field inside the solenoid.

b )

Magnetic field around a very long wire at a distance d is given by the expression

B = ( μ₀ /4π ) X 2I / d

= 10⁻⁷ x 2 x ( 1.75 / .01 )

= .35 x 10⁻⁴ T

In the second case magnetic field is much less. It is due to the fact that in the solenoid magnetic field gets multiplied due to increase in the number of turns. In straight coil this does not happen .

Answer 2

Answer:

a) B = 2.83 mT

b) B1 = 3.5 * 10^-2 mT

Explanation:

Length of solenoid = 35 cm

= 0.35 m

Number of turns for circular coils (N) = 450

diameter = 2.0cm

= 0.02m

Radius = 0.02/2 =0.01

Current = 1.75A

a) Magnetic field is given by;

B = μoNi / l

μo = 4π * 10^-7

B = (4π*10^-7 * 450 * 1.75) / 0.35

B = (9.8960 * 10^-4) / 0.35

B = 2.83mT

The magnetic field at the center of the solenoid, 1.0cm 4th he could is 2.83mT

b) The distance from the centre if a very long wire in d.

d = 1.0cm = 0.01m

Magnetic field(B1) = μoi / 2πd

μo = 4π * 10^-7

B1 = (4π*10^-7 * 1.75) / 2π * 0.01

B1 = (2.2 * 10^-6) / 0.63

B1 = 0.3492 * 10^-4

B1 = 3.5 * 10^-5 T

B1 = 3.5 * 10^-2 mT

The two magnetic fields are not the same. This is because in the first magnetic field, the solenoid magnetic field is multiplied due to increase in the number of turns but it is not the same for the straight coil