What is the formula for a magnetic field due to a finite wire with current?

In summary, a rectangular loop with dimensions 4.20 cm by 9.50 cm carries current I, which produces a magnetic field at the center of the loop with magnitude 3.60×10−5T and direction away from the viewer. To calculate the magnetic field, the general formula for a finite wire with current must be used, which is b = mu_0 I L/ 4pi*r, where l is (a/bsqrt(a^2+b^2)) and (b/asqrt(a^2+b^2)). The given values of a = 0.042m and b = 0.095m can then be plugged into the formula to solve for I.
  • #1
meaghan
15
1

Homework Statement



A rectangular loop with dimensions 4.20 cm by 9.50 cm carries current I. The current in the loop produces a magnetic field at the center of the loop that has magnitude 3.60×10−5T and direction away from you as you view the plane of the loop.

Homework Equations


b = mu_0 I L/ 4pi*r ,where l is (a/bsqrt(a^2+b^2)) and
(b/asqrt(a^2+b^2));
a = .042m
b = .095m

The Attempt at a Solution


i think i just put the given values into the equation, then solve for I, but I'm not sure if I'm setting it up right
 
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  • #2
First write out the general formula for a magnetic field due to a finite wire with current. The formula you write there is not correct.
 

What is the Biot Savart Law?

The Biot Savart Law is a fundamental law in electromagnetism that describes the magnetic field created by a steady current in a conductor.

What is the equation for the Biot Savart Law?

The equation for the Biot Savart Law is B = (μ0/4π) * (I * dl x r)/r^3, where B is the magnetic field, μ0 is the permeability of free space, I is the current, dl is a small segment of the current-carrying conductor, r is the distance between the segment and the point where the magnetic field is measured, and x represents the vector cross product.

How is the Biot Savart Law used in practice?

The Biot Savart Law is used in various applications, such as calculating the magnetic field of a wire or a solenoid, designing magnetic sensors, and understanding the motion of charged particles in a magnetic field.

What are the limitations of the Biot Savart Law?

The Biot Savart Law is only valid for steady currents in conductors. It does not take into account the effects of changing electric fields or magnetic materials. Additionally, it assumes that the magnetic field is created by an infinitesimal element, which may not always be the case in real-world scenarios.

Who discovered the Biot Savart Law?

The Biot Savart Law was discovered by French physicists Jean-Baptiste Biot and Félix Savart in the early 19th century. They conducted experiments to measure the magnetic field around a current-carrying wire and derived the mathematical relationship between the current and the magnetic field.

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