Current loop Definition and 104 Threads

I have attempted to solve it as follows: Using the Biot-Savart law, I found the flux density at the centre of the smaller coil due to the bigger coil as: $$\frac{\mu_0 I b^2 N_2}{2(a^2 + b^2)^{1.5}}$$ where a is the distance to the coil (10cm), N2 is the number of loops in the larger coil (50)...

Hi all, my work is shown on the attached image. The boxed equation is what I get to but I do not understand how to go from there to what the book has. I am guessing that the problem arises when trying to solve the cross product. I understand that I will need to find the value of the sine of the...

The energy stored in a current loop equals ##\frac{LI^2}{2}##. From a dimensional argument, it follows that the inductance grows with the size of the loop. This would mean that, if we assume the current stays constant, enlarging the loop would require external positive work, so, the force...

This should be pretty straightforward and my take gives B = 0.000193*T for a) and B = 0.00000063 T for b). Or have I misunderstood something?

Okay, so, the magnetic field lying(parallel) to the plane of the coil is confusing me quite a bit. Usually, in this kind of problem, we have a magnetic field directed perpendicularly to the plane. Considering this orientation of the field, wouldn't the torque on this sort of "elementary brush...

Disclaimer: The solution to this question has already been posted by my instructor. I made this post to understand why my solution is wrong or if the instructor is wrong, since their explanation does not make sense to me. My reasoning: Using the fact that the magnetic torque on a...

##\vec \tau = \vec \mu \times \vec B -eq1## ## F = I \vec l \times \vec B -eq2 ## The forces i have indicated The magnetic moment is coming out of the page. I am only attempting only the part (a) as of now a. The force calculations are F1 = 1.4*0.22*1.5 = 0.462 +X direction F2 = 1.4*0.22*1.5...

Can anyone please tell me why the torque on a circular current loop can be calculated by the equation below? In other words, what is the intuition for the formula? Thank you. (I modified my question to a particular case) $$ \vec{\tau} = I \vec{A} \times \vec{B} $$

In the attached picture, I’ve drawn a crude schematic of the motor circuit. It is fed from a switchgear feeding 3 total motors. The feed contains 2 parallel conductors on each phase and ground. The equipment ground reads 12a going back to the switchgear, 6a per conductor. From the starter to...

So I'm having a little trouble getting to the solution to this question so here's my attempt at a solution and I'm not seeing the issue with it 1. I calculated the B-field due to the long wire (approximating the distance from the dipole to be equivalent to that in the centre since r>d) B=...

Hi there, I was recently helping a friend of mine with a fairly standard electromagnetic induction problem (a basic sketch of the set-up is attached) where we have a current loop with resistance ##R## moving through a magnetic dipole and had to roughly sketch out the current induced in the loop...

Homework Statement Discussions of the possibility of a tangential E-field external to a current-carrying conductor must include a voltage source and a return path. Here the problem is reduced to (we believe) the simplest possible geometry. Assume that a circular conducting loop has constant...

Homework Statement [/B] ∇ * B = 0 and ∇ X B = Mu * J. This is proved to hold not only for infinite wires but for magnetostatics in general. Magnetostatics = steady current Closed wire loop with constant current is certainly a magnetostatics example. Magnetic field on z axis above loop around...

Hi Forum I am trying to get a better grasp of the relation between electric field and the magnetic field. The overall question is "What is The origin of selfinductance in a current loop?" Here are my thourghts: A battery is connected to a say circular wire with some resistance. The current...

Homework Statement Find the exact magnetic field a distance z above the center of a square loop of side w, carrying a current I. Verify that it reduces to the field of a dipole, with the appropriate dipole moment, when z >> w. Homework Equations (1) dB = μ0I/4πr2 dl × rhat (2) r =...

Homework Statement A rectangular loop of wire with sides H = 22 cm and W = 77 cm is located in a region containing a constant magnetic field B = 0.82 T that is aligned with the positive y-axis as shown. The loop carries current I = 334 mA. The plane of the loop is inclined at an angle θ = 30°...

Homework Statement Starting from the Lorentz force law, in the form of Fmag = ∫ I (d× B), show that the torque on any steady current distribution (not just a square loop) in a uniform field B is m × B. Homework Equations I looked at the solution I found in this thread here, but I don't...

Hello friends, I am trying to find how calculate the magnetic field created by current loop considering that there is a some geometry of material that can enhance the magnetic field. I thought it can be solved by multipling by permeability μ but realized that the iron core changes the picture of...

I'm asking the above question as I imagined a current loop made out of a curving wire that cannot fit into a flat plane. Where does the direction of μ point then? Also, is there only one μ value for any current loop, independent of the chosen axis of tilting? Or can a current loop have...

A square loop of wire in the x-y plane, centred on the origin, is made up of four straight segments, each of length 2d=10cm. A current I =10A flows in the wire in the direction shown. Find the magnetic field at z=d on the z-axis. (See "Diagram" for the diagram of the problem) Here is the...

Homework Statement [/B] A very thin plastic ring (radius R) has a constant linear charge density, and total charge Q. The ring spins at angular velocity \omega about its center (which is the origin). What is the current I, in terms of given quantities? What is the volume current density J in...

Is it possible to find the magnetic field on the axis above a current loop using Ampere's law? I was thinking you could treat an infinitesimal piece of the loop as a straight wire and draw a circle around it with radius sqrt(a^2 + z^2), with a=radius of current loop and z=position of point of...

Homework Statement How to calculate the magnetic field at the centre of a circular current (I) loop of radius r using Ampere law Homework Equations B = μ0I/2r The Attempt at a Solution I take circulation along the circular closed path of radius r passing through the center of the loop and...

Homework Statement Problem 6.2 of Griffith's "Introduction to Electrodynamics": Starting from the Lorentz force law ##\vec F=\int I (d\vec l \times \vec B)##, show that the torque on any steady current distribution (not just a square loop) in a uniform field ##\vec B## is ##\vec m\times \vec...

There are plenty of examples where someone derives the magnetic force from a current carrying wire on a moving charged particle by looking at the frame of the particle and finding that the current has Lorentz contracted in such a way as to produce an electric field in an otherwise neutral wire...

Homework Statement Hi everyone, My problem is fairly simple: We have a circular current loop enclosing area A, and with a constant current I. The loop is rotating about its diameter at a constant angular frequency \omega. All we need to do is find the electric dipole, and magnetic dipole...

The question states: The calculation of the magnetic moment of a current loop leads to the line integral ∮ r x dr I am puzzled - shouldn't this be ∮ r x dl where r is the radius of the loop and dl is the small change along the loop? (I think dr would be in the same direction as r, so no cross...

I'm trying to understand how to calculate the strength of the magnetic field generated by a current loop. What I know so far is: When a current moves around a loop of wire it generates a magnetic field which looks a bit like that of a solenoid, only not so concentrated through the center of...

Homework Statement A current loops is oriented in three different positions relative to a uniform magnetic field. In position 1, the plane of the loop is perpendicular to the field lines. In position 2 and 3, the plane of the loop is parallel to the field as shown. The torque on the loop is...

Homework Statement A magnetic dipole m is moved from infinitely far away to a point on the axis of a fixed, perfectly conducting (zero resistance) circular loop of radius a and self-inductance L. In its final position the dipole is oriented along the axis of the loop and is a distance z from...

Hello everyone, I want to have a simple example of an inductance calculation. The magnetic field normal to a filamentary circular current loop is not constant over the circle but if we approximate the value as that for the center, multiply by the area of the circle and divide by the current...

I'm trying to get a feel for the overall magnitude of the Earth's magnetic field. If I placed a superconducting belt around the Earth magnetic equator, how much current would that loop have to carry to approximate the Earth magnetic field? Currently, the field at the equator is about 31 microT...

Suppose you want to find the magnetic field at a point p at the z axis from the picture attached. Attempt to understand this problem: The way the books solves it is that it says the angle theta between current element i ds and r is 90. Then he calculates the integeral which has two...

i know that a current loop creates some kind of a short bar magnet , but how ? i mean in a short bar magnet , the magnetic field leaves the north pole and goes towards the south pole Of the MAGNET itself , but in the case of the solenoid or a coil , it just looks as if the magnetic field...

The vector magnetic potential is given \vec A=\frac{\mu I}{4\pi}\oint\frac{e^{-j\beta R_1}}{R_1}dl' After a few steps, the equation becomes: \vec A=\frac{\mu I}{4\pi}e^{-j \beta R}\left[ (1+j\betaR)\oint\frac{dl'}{R_1}-j\beta\oint dl'\right] The Book claim the second integral obviously...

Homework Statement A nonuniform magnetic field exerts a net force on a current loop of radius R. The figure shows a magnetic field that is diverging from the end of a bar magnet. The magnetic field B at the position of the current loop makes an angle θ with respect to the vertical, as the...

Hi, I'm trying to calculate the outward force on a loop of wire carrying a current, radially from the center to the perimeter. I found the formula for the force between two parallel wires: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/wirfor.html F/L = u0*I1*I2/(2*pi*r) And the...

Homework Statement A uniform non-conducting ring of radius 0.816 cm and total charge 6.76 µC rotates with a constant angular speed of 1.73 rad/s around an axis perpendicular to the plane of the ring that passes through its center. What is the magnitude of the magnetic moment of the...

Suppose we have a neutral uncharged square current loop, carrying a constant current I. If we boost it in the x direction, x' = \gamma \left( x + \beta t \right) , so that x' increases as t increases (hence the plus sign), what happens to the current? I get that the current density in the y...

Homework Statement http://pokit.org/get/img/65e8ba92c1d00bf7fc8be2b178757ed8.jpg If a=5b, and I1 and I2 are known, find the force on the triangular loop. Homework Equations The Attempt at a Solution For start, the field from the infinitely long wire is : \vec B=\large -\frac{\mu _{0}...

Homework Statement Prove that, in a uniform magnetic field, the net force on a current loop carrying current I is zero.Homework Equations Green's theorem, and magnetic force equationThe Attempt at a Solution My main question is whether I can use Green's theorem to prove this result... it seems...

Homework Statement Please check the enclosed figure. Find the force of compression in the wire loop. Magnetic field B is directed into the page and current i is flowing anti-clockwise. The radius of the wire loop is 'a'. Homework Equations \vec{F}=i\vec{l}\times\vec{B} The...

Hello, calculating the magnetic moment of a current loop is trivial, but I want to do it with the general formula \vec m = \frac{1}2 \int \vec r \times \vec J(\vec r) d^3\vec r The only thing which is stopping me is to find a good argument on why \frac{1}{2}\int \vec r d\vec r = \vec A where...

Homework Statement A small current loop of area A=0.0008m2 and moment of inertia I=6.9e-07kgm2 carries a current i=0.0039A with its magnetic moment perpendicular to the Earth's magnetic field. The magnitude of the Earth's field is B=4.2e-05T. a). What is the magnitude of the net torque T on...

Homework Statement A triangular loop of side length a carries a current I. If this loop is placed a distance d away from a very long straight wire carrying a current I', determine the force on the loop. See attachment for diagram. Homework Equations F=(\muII'/2\pir)L F=I'LB...

Homework Statement An electron moves in a circle of radius r = 5.29 x 10^-11 m with speed 2.19 x 10^6 m/s. Treat the circular path as a current loop with a constant current equal to the ratio of the electron's charge magnitude to the period of the motion. If the circle lies in a uniform...

I was reasoning about this matter and i found myself asking a question ... i tried to search the answer in quite a number of books (mainly Physics_For_Scientists_And_Engineers_6_Ed._By_Serway_And_Jewett and and Physics_by_James_S_Walker) but no way ... all the information i found are related to...

Homework Statement A rectanglar loop of wire encloses an area A, has a resistance R and a self-inductance L. The loop is suspended from the mid point of one of its sides and placed in a horizontal oscillating magnetic field B = B0 sin ωt such that the field makes an angle θ with the normal to...

Homework Statement See figure attached. Homework Equations The Attempt at a Solution I'm having some confusion about the negative sign within this problem. If you compute the curl of the expression shown in the figure you'll find that it's equal to, -10v_{0} \hat{k} But...

Homework Statement The current loop is in the y-z plane. The direction of the magnetic field is in the z-direction. A) Which way is the torque on the current loop? B) If the current is 4 amps and the magnetic field strength is 2.5 Tesla, what is the magnitude of the torque? here is the...