Circular Loop Center Field

Mediumphysics

Field at center of circular loop radius R carrying current I?

Select the correct option:

μ0 I /(2R)

μ0 I /(4π R)

μ0 I R /2

μ0 /(2 I R)

🔒 Solution Hidden from View

Submit your answer to unlock the detailed step-by-step solution.

About This Question

Subject: physics
Chapter: magnetic effects and magnetism
Topic: circular loop center field
Difficulty: Medium
Year: 2025

Solution

Correct Answer:

μ0 I /(2R)

Biot-Savart Law: $d B = \frac{μ _{0}}{4 π} \frac{I d l s i n θ}{r ^{2}}$ .
Integration for Circle: At the center, every current element $d l$ is at distance $R$ and is perpendicular to the radius ( $θ = 9 0^{\circ}$ ).
Step-by-Step:
- $B = \int \frac{μ _{0}}{4 π} \frac{I d l}{R ^{2}} = \frac{μ _{0} I}{4 π R ^{2}} \int d l$
- Since $\int d l = 2 π R$ (circumference):
- $B = \frac{μ _{0} I}{4 π R ^{2}} \times (2 π R) = \frac{μ _{0} I}{2 R}$ .
Conclusion: The magnetic field strength at the center of the loop is $\frac{μ _{0} I}{2 R}$ .

This medium difficulty physics question is from the chapter magnetic effects and magnetism, covering the topic of circular loop center field. It appeared in the 2025 exam.

Looking for more practice? Explore all physics questions or browse magnetic effects and magnetism questions on RankGuru.

Circular Loop Center Field

Select the correct option:

🔒 Solution Hidden from View

More magnetic effects and magnetism Practice Questions

Ampere's law integral form states ∮ B·dl equals?

Energy density u of magnetic field B in vacuum is?

Horizontal component of Earth's field Bh relates to total B and dip angle δ by?

Differential magnetic field dB due to current element Idl at position vector r (angle θ)?

Magnetic field at distance r from long straight wire carrying current I?

Lorentz force vector expression?

Torque on N-turn rectangular loop area A carrying current I in uniform B (plane at angle θ) equals?

Cyclotron angular frequency ω for charge q, mass m in magnetic field B?

Magnetic field inside long solenoid (turns per length n, current I) approximately?

Magnitude of magnetic force on charge q moving with velocity v perpendicular to uniform B?

Magnetic moment of single current loop (current I, area A)?

Hysteresis loop area represents?

About This Question

Solution