Question

A circular coil $A$ has a radius $R$ and the current flowing through it is $I$. Another circular coil $B$ has radius $2 R$ and if $2 I$ is the current flowing through it, then the magnetic field at the centre of the circular coil are in the ratio of (A) $4: 1$ (B) $2: 1$ (C) $3: 1$ (D) $1: 1$

Name: Problem 7, Chapter 15: A Complete Resource Book in Physics for JEE Main
Uploaded: 2021-10-06T08:12:00-08:00
Duration: 1 min 59 s
Channel: Aja S
Description: A circular coil A has a radius R and the current flowing through it is I. Another circular coil B has radius 2 R and if 2 I is the current flowing through it, then the magnetic field at the centre of the circular coil are in the ratio of (A) 4: 1 (B) 2: 1 (C) 3: 1 (D) 1: 1

   A circular coil $A$ has a radius $R$ and the current flowing through it is $I$. Another circular coil $B$ has radius $2 R$ and if $2 I$ is the current flowing through it, then the magnetic field at the centre of the circular coil are in the ratio of
(A) $4: 1$
(B) $2: 1$
(C) $3: 1$
(D) $1: 1$

A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar 1st Edition

Chapter 15, Problem 7

Instant Answer

Solved by Expert Aja S

10/06/2021

Step 1

Step 1: The magnetic field at the center of a circular coil is given by the formula $B = \frac{\mu_0 I}{2R}$, where $I$ is the current flowing through the coil, $R$ is the radius of the coil, and $\mu_0$ is the permeability of free space. Show more…

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A circular coil $A$ has a radius $R$ and the current flowing through it is $I$. Another circular coil $B$ has radius $2 R$ and if $2 I$ is the current flowing through it, then the magnetic field at the centre of the circular coil are in the ratio of (A) $4: 1$ (B) $2: 1$ (C) $3: 1$ (D) $1: 1$

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Key Concepts

Magnetic Field of a Circular Loop

This concept refers to the magnetic field produced at the center of a circular wire due to an electric current flowing through it. The general formula for this field is derived from the Biot–Savart law and is given by B = (?? * I) / (2 * R), where I is the current and R is the radius of the loop.

Dependence on Current and Radius

This key concept explains that the magnetic field at the center of a circular loop is directly proportional to the current and inversely proportional to the radius of the loop. Increasing the current while keeping the radius constant will proportionally increase the magnetic field, whereas increasing the radius with a constant current will decrease the magnetic field.

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