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A solenoid with an iron core is 25 cm long and is wrapped with 100 turns of wire. When the current through the solenoid is 10 A, the magnetic field inside it is 2.0 T. For this current, what is the permeability of the iron? If the current is turned off and then restored to 10 A, will the magnetic field necessarily return to 2.0 T?

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Additional problems

Three long, straight, parallel wires, all carrying 20 A, are positioned as shown in the accompanying figure. What is the magnitude of the magnetic field at the point P ?

This figure shows three long, straight, parallel wires. Each wire forms a vertex of an equilateral triangle with 10 centimeter sides. Point P is the center of a triangle.

B = 6.93 × 10 −5 T

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A current I flows around a wire bent into the shape of a square of side a . What is the magnetic field at the point P that is a distance z above the center of the square (see the accompanying figure)?

This figure shows a wire bent into the shape of a rhombus of side a. Point P that is a distance z above the center of the rhombus.
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The accompanying figure shows a long, straight wire carrying a current of 10 A. What is the magnetic force on an electron at the instant it is 20 cm from the wire, traveling parallel to the wire with a speed of 2.0 × 10 5 m/s? Describe qualitatively the subsequent motion of the electron.

Figure shows a long, straight wire carrying a current. An electron is located 20 cm from the wire and travels parallel to it.

3.2 × 10 −19 N in an arc away from the wire

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Current flows along a thin, infinite sheet as shown in the accompanying figure. The current per unit length along the sheet is J in amperes per meter. (a) Use the Biot-Savart law to show that B = μ 0 J / 2 on either side of the sheet. What is the direction of B on each side? (b) Now use Ampère’s law to calculate the field.

Figure shows current flowing along a thin, infinite sheet.
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(a) Use the result of the previous problem to calculate the magnetic field between, above, and below the pair of infinite sheets shown in the accompanying figure. (b) Repeat your calculations if the direction of the current in the lower sheet is reversed.

Figure shows currents flowing along two thin, infinite sheets. Sheets are located in the parallel planes and current flows in the same direction.

a. above and below B = μ 0 j , in the middle B = 0 ; b. above and below B = 0 , in the middle B = μ 0 j

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We often assume that the magnetic field is uniform in a region and zero everywhere else. Show that in reality it is impossible for a magnetic field to drop abruptly to zero, as illustrated in the accompanying figure. ( Hint : Apply Ampère’s law over the path shown.)

Figure shows the magnetic field that is perpendicular to the rectangular current path and intersects it.
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How is the percentage change in the strength of the magnetic field across the face of the toroid related to the percentage change in the radial distance from the axis of the toroid?

d B B = d r r

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Show that the expression for the magnetic field of a toroid reduces to that for the field of an infinite solenoid in the limit that the central radius goes to infinity.

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A toroid with an inner radius of 20 cm and an outer radius of 22 cm is tightly wound with one layer of wire that has a diameter of 0.25 mm. (a) How many turns are there on the toroid? (b) If the current through the toroid windings is 2.0 A, what is the strength of the magnetic field at the center of the toroid?

a. 52778 turns; b. 0.10 T

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A wire element has d l , I d l = J A d l = J d v , where A and dv are the cross-sectional area and volume of the element, respectively. Use this, the Biot-Savart law, and J = n e v to show that the magnetic field of a moving point charge q is given by:
B = μ 0 4 π q v × r ^ r 2

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A reasonably uniform magnetic field over a limited region of space can be produced with the Helmholtz coil, which consists of two parallel coils centered on the same axis. The coils are connected so that they carry the same current I . Each coil has N turns and radius R , which is also the distance between the coils. (a) Find the magnetic field at any point on the z -axis shown in the accompanying figure. (b) Show that dB / dz and d 2 B d z 2 are both zero at z = 0. (These vanishing derivatives demonstrate that the magnetic field varies only slightly near z = 0.)

This picture shows two parallel coils centered on the same axis that carry the same current I. Each coil has radius R, which is also the distance between the coils.

B 1 ( x ) = μ 0 I R 2 2 ( R 2 + z 2 ) 3 / 2

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Questions & Answers

A glass bottle full of mercury has mass 50g when heated through 35degree, 2.43g of mercury was expelled. Calculate the mass of the mercury remaining in the bottle
Anjorin Reply
Two electric point charges Q=2micro coulomb are fixed in space a distance 2.0cm apart. calculate the electric potential at the point p located a distance d/2 above the central point between two charges
Abdul Reply
what is wave
Ahmed Reply
What is charge bodies
Oje Reply
which have free elections
Usman
Show that if a vector is gradient of a scaler function then its line around a closed path is zero
Pak
Charge bodies are those which have free electons
Pak
the melting point of gold is 1064degree cencius and is boiling point is 2660 degree cenciu
Ilyas Reply
is Thomas's young experiment interference experiment or diffraction experiment or both
Ilyas Reply
An aqueous solution is prepared by diluting 3.30 mL acetone (d = 0.789 g/mL) with water to a final volume of 75.0 mL. The density of the solution is 0.993 g/mL. What is the molarity, molality and mole fraction of acetone in this solution?
eugene
A 4.0kg mess kit sliding on a fractionless surface explodes into two 2.0 kg parts.3.0 m/s due to north and 0.5 m/s 30 degree north of east. what is the speed of the mess kit
Shahid
it's a line used to represent a complex electrical quantity as a vector
Gift Reply
what is the meaning of phasor?
fitness Reply
The electric field inside a sphere of radius is given by the expression for some constants and. Find the charge density and the total charge contained in this sphere.
maloda Reply
what is motion?
Abdulaziz Reply
is the change of position of body
Kate
it's the process of moving something.
Gift
the state of a body in which it change its position with respect to sorrounding is known as motion for example player of football change its position with respect to spectator
Ilyas
it is a state of body in which it changes it,s position with respect to their time and immediate surrounding
Harish
a particle change with respect to time and position
Babak
it is a stat of body in which it changes its position with respect to mean and exstrem position
Manzoor
A 4.0 kg mass kit sliding on a fractionless surface explodes into two 2.0 kg parts,3.0 m/s due to north and 0.5 m/s 30 degree north of east. what the speed of mass kit
Shahid
momentum conservation
Mehmet
3.5 m/s north of east.
Mehmet
give me a compete solution
Shahid
where the solving of questions of this topic?
Bonifasi Reply
According to Nernst's distribution law there are about two solvents in which solutes undergo equilibria. But i don't understand how can you know which of two solvents goes bottom and one top? I real want to understand b'coz some books do say why they prefer one to top/bottom.
Elia Reply
I need chapter 25 last topic
Hafsa Reply
What is physics?
Abdulaziz
physics is the study of matter and energy in space and time and how they related to each other
Manzoor
interaction of matter and eneegy....
Abdullah
thanks for correcting me bro
Manzoor
What is electrostatics bassically?
Ehtisham Reply
study of charge at rest
wamis
A branch in physics that deals with statics electricity
Akona
what is PN junction?
Manzoor
please I don't understand the solution of the first example as in d working
habila Reply
what's the question? Write it here.
SABYASACHI
Practice Key Terms 6

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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