# How Does the Biot-Savart Law Apply to Uneven Currents in a Split Loop?

• GDGirl
In summary, a circular conducting ring with two exterior straight wires connected to its ends has an uneven current split, with I1 = 3.8 A passing through the top semicircle and I2 = 10 A passing through the lower semicircle. To find the magnetic field at the center of the ring, the Biot-Savart Law is used for each semicircle, taking into account the signs of the resulting B fields. The direction of the currents in the two semicircles is not the same, leading to different signs for the B fields. The correct method for finding the direction of the magnetic field due to a current carrying conductor is to determine whether the current is flowing clockwise or counterclockwise in the
GDGirl

## Homework Statement

A circular conducting ring or radius R = 10.7 cm is connected to two exterior straight wires ending at two ends of a diameter (see Figure). The current splits into uneven portions, with I1 = 3.8 A passing through the top semicircle, and I2 = 10 A passing through the lower semicircle. What is B at the center of the ring?
HELP: Apply the Biot-Savart Law to each semicircle. Adding the two resulting B fields, being careful to keep track of their signs.
https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/Knox/phys130a/spring/homework/14/02/P28_31.jpg

## Homework Equations

B=$$\mu$$0I($$\pi$$r)/4$$\pi$$r2 (for each half circle)

## The Attempt at a Solution

I used the equation I put above, and found that the B field for the first current was 1.114e-5 (B1=(4$$\pi$$x10-7)(3.8)/(4$$\pi$$)(.10702 ($$\pi$$.107)) and the second current gave me 2.935e-5. From there I tried simply adding them, to give me a total of 4.049e-5. This is incorrect. So I figured they might be vectors, and tried using pythagorean on them ($$\sqrt{(1.114e-5)^2+(2.935e-5)^2}$$) and got 3.139e-5. this is also incorrect.
I figure I'm doing something wrong, but I'm not sure what. The hint says to be sure to pay attention to the signs of the B fields, but I don't see where I would get something other than a positive sign.

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What is the method of finding the direction of the magnetic field due to current carrying conductor?
Since the directions of the current in two semicircles is not the same, the signs of the fields must be different.

rl.bhat said:
What is the method of finding the direction of the magnetic field due to current carrying conductor?
Since the directions of the current in two semicircles is not the same, the signs of the fields must be different.

But aren't the directions the same? Both currents are going to the right.

In semicircle direction should be either clockwise or counterclockwise.

Oh. Okay, I got it now, thanks. :)

## 1. What is Biot-Savart Law?

The Biot-Savart Law is a fundamental law in electromagnetism that describes the magnetic field generated by a steady electric current. It was named after French scientists Jean-Baptiste Biot and Félix Savart who first described the relationship between electric currents and magnetic fields in 1820.

## 2. How does Biot-Savart Law apply to a split loop?

In the context of a split loop, the Biot-Savart Law states that the magnetic field at any point in space due to a current carrying split loop can be calculated by summing the contributions from each segment of the loop using a mathematical formula. This allows us to determine the strength and direction of the magnetic field at any point surrounding the loop.

## 3. What factors affect the strength of the magnetic field in Biot-Savart Law?

The strength of the magnetic field in Biot-Savart Law is affected by the magnitude of the current, the distance from the current-carrying element to the point where the field is being measured, and the angle between the current and the line connecting the current element to the point where the field is being measured.

## 4. How is Biot-Savart Law used in practical applications?

Biot-Savart Law has many practical applications, such as in designing electromagnets, electric motors, and generators. It is also used in medical imaging techniques like magnetic resonance imaging (MRI) and in studying the Earth's magnetic field. It is a fundamental principle that helps us understand and manipulate the behavior of magnetic fields.

## 5. Is Biot-Savart Law a special case of Ampere's Law?

No, Biot-Savart Law and Ampere's Law are two separate laws that describe different aspects of electromagnetism. While Ampere's Law relates the magnetic field to the current enclosed by a closed loop, Biot-Savart Law deals with the magnetic field due to a small current element. Both laws are essential in understanding the behavior of magnetic fields in different scenarios.

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