How to find the magnetic field and magnetic force due to a solenoid loop

In summary, the problem is to calculate the magnetic field B at a solid conductor point of length ##l## at a distance ##d## from a rectangular coil with ##N## turns, using the Biot-Savart Law. The field on the conductor due to the parallel segments of the coil is zero according to Ampere's Law, and for the perpendicular segments, the field of a ring of radius ##R## at a point ##d## from its center is used. The final integration yields ##\vec B= \frac{\mu_0nI_2}{2}\cdot \frac{l^2}{(l^2+R^2)^{1/2}}\hat z##. The Lorentz
  • #1
Davidllerenav
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Homework Statement
For the rectangular coil of ##N## turns and with
the dimensions shown in figure 1,
calculate the magnetic field B that occurs
at a solid conductor point of length ##l##
at a distance d from the coil. Consider that
The current flowing through the coil is ##I_2##.
Relevant Equations
Biot-Savart Law: ##\vec B= \frac{\mu_0}{2\pi}\int \frac{d\vec l \times \hat r}{r^2}##
1574133101522.png

I'm not so sure how to begin with this problem. I was thinking of usign superposition. I think that the field on the conductor due to the parallel segments of the coil is zero, since Ampere's Law tells us that the field outside the solenoid is zero, right? For the perpendicular segments, I used the field of a ring of radius ##R## at a point a distance ##d## from its center and I integrated, getting ##\vec B= \frac{\mu_0nI_2}{2\pi}\int_0^l \frac{R^2dz}{(R^2+d^2)^{3/2}}=\frac{\mu_0nI_2}{2}\cdot \frac{l^2}{(l^2+R^2)^{1/2}}\hat z##. Am I correct?
 
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  • #2
Davidllerenav said:
Homework Statement: For the rectangular coil of ##N## turns and with
the dimensions shown in figure 1,
calculate the magnetic field B that occurs
at a solid conductor point of length ##l##
at a distance d from the coil. Consider that
The current flowing through the coil is ##I_2##.
Homework Equations: Biot-Savart Law: ##\vec B= \frac{\mu_0}{2\pi}\int \frac{d\vec l \times \hat r}{r^2}##

View attachment 253023
I'm not so sure how to begin with this problem. I was thinking of usign superposition. I think that the field on the conductor due to the parallel segments of the coil is zero, since Ampere's Law tells us that the field outside the solenoid is zero, right? For the perpendicular segments, I used the field of a ring of radius ##R## at a point a distance ##d## from its center and I integrated, getting ##\vec B= \frac{\mu_0nI_2}{2\pi}\int_0^l \frac{R^2dz}{(R^2+d^2)^{3/2}}=\frac{\mu_0nI_2}{2}\cdot \frac{l^2}{(l^2+R^2)^{1/2}}\hat z##. Am I correct?
Biot-Savart is the general law for finding the B field due to arbitrary current distributions.
You want the force exerted on a wire carring current due to an externally applied B field (like that of a second wire, hint hint). This is a vector relation so if for example the B field is generated by a second wire you need to consider the relative orientation between the two wires.
What you're looking for is in every intro physics text. Better yet, you can derive it yourself by starting with the expression for the Lorentz force F = qv x B and yes, combining with Ampere's law.. Forces can be added (vectorially of course).
 
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FAQ: How to find the magnetic field and magnetic force due to a solenoid loop

1. How do you calculate the magnetic field of a solenoid loop?

To calculate the magnetic field of a solenoid loop, you can use the equation B = μ₀nI, where μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current flowing through the solenoid. You can also use the equation B = μ₀nI/l, where l is the length of the solenoid.

2. What is the direction of the magnetic field inside a solenoid loop?

The magnetic field inside a solenoid loop is always parallel to the axis of the loop and is directed from the north pole to the south pole.

3. How do you find the magnetic force on a charged particle moving through a solenoid loop?

You can find the magnetic force on a charged particle moving through a solenoid loop by using the equation F = qvBsinθ, where q is the charge of the particle, v is its velocity, B is the magnetic field, and θ is the angle between the velocity and the magnetic field.

4. How does the magnetic field inside a solenoid loop change with increasing current?

The magnetic field inside a solenoid loop is directly proportional to the current flowing through the loop. As the current increases, the magnetic field also increases.

5. Can the magnetic field inside a solenoid loop be uniform?

Yes, the magnetic field inside a solenoid loop can be made to be nearly uniform by increasing the number of turns per unit length or by increasing the length of the solenoid. However, it is not completely uniform due to the fringing effect at the ends of the solenoid.

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