Physics, 10.03.2020 02:09, bubblegum2850

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.

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answered: j0162

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

$B=\int{\dfrac{\mu_{0}}{4\pi}\times\dfrac{I\times dl}{R^2}}$

$B=\dfrac{\mu_{0}I}{4\pi\times R^2}\int{dl}$

Put the value into the formula

$B=\dfrac{\mu_{0}I}{4\pi\times r^2}\times2\pi R$

$B=\dfrac{\mu_{0}I}{2R}$ ...(I)

We need to calculate the magnetic field due to solenoid

Using formula of magnetic field

$B'=\mu_{0}nI$ ...(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)

$\dfrac{B'}{B}=\dfrac{\mu_{0}nI}{\dfrac{\mu_{0}I}{2R}}$

$\dfrac{B'}{B}=2nR$

Put the value into the formula

$\dfrac{B'}{B}=2\times2000\times20\times10^{-3}$

$\dfrac{B'}{B}=80$

B'=80 B

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.

answered: Guest

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm. the wire diameter is d = 0.9 mm. the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2) in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

answered: Guest

what was the acceleration of the 2 kg cart?

⇒ 16.0 cm/s2

what was the acceleration of the 4 kg cart?

⇒ 8.1 cm/s2

what was the acceleration of the 6 kg cart?

⇒ 5.3 cm/s2

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Compare the magnitude of the magnetic field at the center of a circular current loop of radius 20 mm...