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

  • Thread starter Thread starter GDGirl
  • Start date Start date
  • Tags Tags
    Law Loop Split
AI Thread Summary
The discussion focuses on applying the Biot-Savart Law to calculate the magnetic field at the center of a circular conducting ring with uneven current distribution. The currents are I1 = 3.8 A in the top semicircle and I2 = 10 A in the bottom semicircle. Initial calculations for the magnetic fields from each semicircle yielded incorrect results when simply added. The key point is recognizing that the directions of the currents in the semicircles differ, affecting the signs of the resulting magnetic fields. Understanding the correct vector addition and direction of the magnetic fields is crucial for obtaining the accurate total magnetic field.
GDGirl
Messages
49
Reaction score
0

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=\mu0I(\pir)/4\pir2 (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\pix10-7)(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.
 
Last edited by a moderator:
Physics news on Phys.org
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. :)
 
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanged mass'

Thread 'A cylinder connected to a hanged mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Force Between 2 Coaxial Current-Carrying Loops
Replies
4
Views
1K
Magnetic field at origin due to infinite wires and semicircular turn
Replies
3
Views
2K
Calculating magnetic field outside a solenoid
Replies
15
Views
1K
Biot-Savart's Law for cylindrical conductor
Replies
18
Views
5K
What is the B-field at the center of a semicircle using the Biot-Savart Law?
Replies
3
Views
4K
Biot-Savart and a Rectangular Loop
Replies
3
Views
3K
Biot-Savart Law with two semi-circles
Replies
1
Views
7K
Can the Biot-Savart Law be applied to point P_1 outside a finite wire?
Replies
3
Views
3K
How Does Induced Current Change with Loop Acceleration Through a Magnetic Field?
Replies
8
Views
1K
How to find the magnetic field and magnetic force due to a solenoid loop
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top