A 36.5 mA current is carried by a uniformly wound air-core solenoid with 430 turns, a...
A 36.5 mA current is carried by a uniformly wound air-core solenoid with 430 turns, a 18.5 mm diameter, and 11.5 cm length.
(a) Compute the magnetic field inside the solenoid.
(b) Compute the magnetic flux through each turn.
(c) Compute the inductance of the solenoid.
mH
(d) Which of these quantities depends on the current? (Select all that apply.)
magnetic field inside the solenoid
magnetic flux through each turn
inductance of the solenoid
Solutions
Expert Solution
Concepts and reason
The concept required to solve this problem are magnetic field inside a solenoid, magnetic flux, and self-inductance.
Initially, use the formula of magnetic field to solve for the magnetic field inside the solenoid.
Later, solve for the area and substitute in the magnetic flux equation to calculate the magnetic flux through each turn of the solenoid. Then calculate the self-inductance of the solenoid from the equation of self-inductance.
Finally, simplify the expressions of magnetic field, flux and self-inductance to identify the quantities that depends on the current in the coil.
Fundamentals
The expression for magnetic field B inside the solenoid is given as follows:
B=μ0lNi
Here, μ0 is the permeability of vacuum, N is the number of turns of the solenoid, l is the length of the solenoid and i is the current through the solenoid.
The magnetic flux through the coil is given as follows:
Φ=BA
Here, B is the magnetic field, and A is the area of the coil.
The area of the circular cross section of cylinder is,
A=πr2
Here, r is the radius of solenoid.
The self-inductance of the solenoid is given as,
L=INΦ
Here, μ0 is the permeability of vacuum, N is the number of turns of the solenoid, A is the area of cross section of the solenoid, and l is the length of the solenoid.
(a)
Use the equation of magnetic field due to a solenoid at its center.
Substitute 4π×10−7T⋅m/A for μ0 , 430 for N, 11.5 cm for l , and 36.5mA for i in the equation B=μ0lNi and calculate the magnetic field inside the solenoid.
A solenoid wound with 2020 turns/m is supplied with current that
varies in time according to I = (4 A)sin(120πt), where t is in s. A
small coaxial circular coil of 40 turns and radius r = 4.1 cm is
located inside the solenoid near its center. (a) Derive an
expression that describes the manner in which the emf in the small
coil varies in time. (Use the following as necessary: t.) (b) At
what average rate is energy transformed...
A long solenoid (1500 turns/m) carries a current of 20 mA and
has an inside diameter of 4.0 cm. A long wire carries a
current of 2.0 A along the axis of the solenoid. What is
the magnitude of the magnetic field at a point that is inside the
solenoid and 1.0 cm from the wire?
a. 78 µ
b. 55 µT
c. 48 µT
d. 68 µT
e. 2.0 µT
A long solenoid has 110 turns/cm and carries current i. An
electron moves within the solenoid in a circle of radius 2.54 cm
perpendicular to the solenoid axis. The speed of the electron is
0.0635c (c = speed of light, equal to 2.998 × 108 m/s). Find the
current i in the solenoid.
a) Assume that there is a long ideal solenoid with 120 turns/cm.
It carries a current i= 2 A and it has a diameter 2 cm and a length
5 m. Find the uniform magnetic field inside the solenoid.
c) Now, construct an RL circuit using an ideal battery
that has potential difference 5 V, one resistor with R = 2 Ω and
the solenoid that has same shape with one mentioned at part (a).
Wait very long time and...
A solenoid with 2000 turns/meter is connected to a power source
that delivers an increasing current i60t^2 Ampere.The solenoid has
a length of 0.2 m and a radius of 0.05 m.
a.what is the magnetic field as a function of timr inside the
solenoid?
b.Use Faraday's law to find the induced emf caused by this
changing magnetic field.
A long, thin solenoid has 870 turns per meter and radius 3.00cm
. The current in the solenoid is increasing at a uniform rate of
65.0A/s .
A)What is the magnitude of the induced electric field at a point
0.550cm from the axis of the solenoid?
B)What is the magnitude of the
induced electric field at a point 1.00cm from the axis of the
solenoid?
A long, thin solenoid has 600 turns per meter and radius 2.6 cm.
The
current in the solenoid is increasing at a uniform rate
dI/dt. The induced
electric eld at a point near the center of the solenoid and 3.80 cm
from
its axis is 8.00 10 -5 V/m. Calculate
dI/dt
An ideal solenoid, of radius R and n turns per unit length, has
a current flowing through it. The current, I, varies with time, t,
according to I = I0 + at where I0 and a are constants. A conducting
ring of radius, r, is placed inside the solenoid with its axis
coinciding with the axis of the solenoid. The ring has a resistance
per unit length of H (in units of Ω/m).
(a) Use Lenz’s law to determine the...
A long, thin solenoid has 870 turns per meter and radius 2.70 cm
. The current in the solenoid is increasing at a uniform rate of
64.0 A/s
What is the magnitude of the induced electric field at a point
0.520 cm
from the axis of the solenoid? (in V/m)
What is the magnitude of the induced electric field at a point
1.30 cm
from the axis of the solenoid? (in V/m)
A closely wound, circular coil with radius 2.10cm
has 830 turns.
A.
What must the current in the coil be if the magnetic field at the
center of the coil is 5.0010-2
B.
At what distance x
from the center of the coil, on the axis of the coil, is the
magnetic field half its value at the center?