Two circular current-carrying loops carry the same current but have different radii. Which loop produces the stronger magnetic field at its center?
The loop with smaller radius produces a larger magnetic field
To determine which circular current-carrying loop produces a stronger magnetic field at its center, we use the formula for the magnetic field at the center of a loop carrying a current \(I\) with radius \(r\):
\(B = \frac{{\mu_0 I}}{{2r}}\)
Where:
- \(B\) is the magnetic field at the center of the loop.
- \(\mu_0\) is the permeability of free space.
- \(I\) is the current through the loop.
- \(r\) is the radius of the loop.
From this formula, it's evident that the magnetic field \(B\) is inversely proportional to the radius \(r\). This implies that as the radius decreases, the magnetic field increases for the same current.
Now, analyze the given options:
- Both loops produce the same magnetic field: Incorrect, because different radii result in different magnetic fields according to the formula.
- The loop with smaller radius produces a larger magnetic field: Correct, because the magnetic field is inversely proportional to the radius.
- The magnetic field at the center is zero: Incorrect, as a circular loop with a current does produce a magnetic field at its center.
- The loop with smaller radius produces a smaller magnetic field: Incorrect, due to the inverse relationship between radius and the magnetic field strength.
Hence, the correct answer is that the loop with the smaller radius produces a larger magnetic field.
Similar Questions
Which of the following statements best describes the behavior of magnetic field lines around a straight current-carrying conductor?
A factory plans to install a powerful electromagnet for lifting metal scraps. To maximize the magnetic field strength around the coil, which of the following combinations would be most effective?
- A student wants to compare the magnetic field patterns produced by a straight current carrying wire and a current-carrying circular loop. Which experimental setup would bestdemonstrate the difference in their magnetic field lines?
- The magnetic field lines around an infinitely long straight current-carrying wire are _________.
A compass needle placed in a uniform magnetic field oscillates about its equilibrium position. What is the main reason for this behavior?
Which of the following statements correctly describe similarities between a bar magnet and a current-carrying solenoid?
1. Both have North and South poles.
2. Both produce a nearly uniform magnetic field inside.
3. Both require permanent magnetic material only.
4. Both follow the right-hand rule for determining the direction of the magnetic field.
Which of the following statements correctly describe magnetic field lines around a bar magnet?
1. Outside the magnet, field lines go from North to South.
2. Inside the magnet, field lines go from North to South.
3. Magnetic field lines always form closed loops.
4. Magnetic field lines are discontinuous at the poles.
Important Questions from Magnetism
How many of the following materials can be attracted by a magnet?
1. Plastic
2. Carbon
3. Aluminium
4. Stainless Steel
Select the correct answer using the code given below:
What will happen if a collection of positive and negative charges are passed at a high speed through a magnetic field which is perpendicular to the direction of motion of the charges? (Assume that both kind of charges are NOT going to recombine)
Which scientist suggested that the magnet must also exert an equal and opposite force on the current-carrying conductor?
Paramagnetic substances are-
The magnetic field lines produced inside a long current-carrying solenoid is similar to that of a:
