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Magnetic Field Due To Circular Current Loop - Practice Questions & MCQ

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

Quick Facts

  • Magnetic Field due to circular current loop is considered one the most difficult concept.

  • 56 Questions around this concept.

Solve by difficulty

A current i ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is

Two concentric coils each of radius equal to  2\pi cm are placed at right angles to each other. 3 ampere and 4 ampere are the currents flowing in each coil respectively. The magnetic induction in weber/m2  at the center of the coils will be

(\mu_{0} =4\pi \times 10^{-7}\; Wb/A-m)

A current loop consists  of two identical semicirular parts each of radius R, one lying in the x-y plane and the other in x-z plane. If the current in the loop is i., the reultant magnetic field due to the two semicircular parts at their commom centre is

Concepts Covered - 1

Magnetic Field due to circular current loop

Magnetic Field due to circular current loop at its centre: 

Magnetic Field due to circular coil at Centre-

B_0=B_{Centre}=\frac{\mu_{0}}{4\pi }\frac{2\pi Ni}{r}=\frac{\mu_{0} Ni}{2r}

where N=number of turns, i= current and r=radius of a circular coil.

Similarly, if  Arc subtends angle theta at the centre as shown below then 

B_0=\frac{\mu_{0}}{4\pi }.\frac{\theta i}{r}

 

similarly, if Arc subtends angle (2\pi-\theta) at the centre then

B_0=\frac{\mu_{0}}{4\pi }.\frac{(2\pi -\theta)i}{r}

So the magnetic field of Semicircular arc at the centre is 

B_0= \frac{\mu_{o}}{4\pi} \:\frac{\pi i}{r}= \frac{\mu_{o}i}{4r}

So Magnetic field due to three quarter Semicircular Current-Carrying arc at the centre is 

B_0=\frac{\mu_{o}}{4\pi}\:\frac{(2\pi-\frac{\pi}{2})i}{r}

  • The direction of the magnetic field-

Right-Hand Thumb Rule gives the direction of the magnetic field of Circular Currents.

Right-hand thumb rule stated below:

If the fingers are curled along the current, the stretched thumb will point towards the magnetic field.

1. If the current is in a clockwise direction then the direction of the magnetic field is away from the observer or perpendicular inwards.

2. If the current is in anti-clockwise direction then the direction of the magnetic field is towards the observer or perpendicular outwards

  • Special cases-

1. If the  Distribution of current across the diameter-

  then B_0=0

2. if Current between any two points on the circumference-

Then B_0=0

 

3.Concentric co-planar circular loops carrying the same current in the Same Direction-

 

  

B_{centre}=\frac{\mu_{o}}{4\pi}\:2\pi i[\frac{1}{r_{1}}+\frac{1}{r_{2}}]

If the direction of currents are the same in concentric circles but having a different number of turns then 

B_{centre}=\frac{\mu_{o}}{4\pi}\:2\pi i[\frac{n_1}{r_{1}}+\frac{n_2}{r_{2}}]

 

 

4.Concentric co-planar circular loops carrying the same current in the opposite Direction-

 

B_{centre}=\frac{\mu_{o}}{4\pi}\:2\pi i[\frac{1}{r_{1}}-\frac{1}{r_{2}}]

 

If the number of turns is not the same i.e n_1\neq n_2

B_{centre}=\frac{\mu_{o}}{4\pi}\:2\pi i[\frac{n_1}{r_{1}}-\frac{n_2}{r_{2}}]

5.  Concentric loops but their planes are perpendicular to each other-

Then B_{net}=\sqrt{{B_{1}}^2+{B_2}^2}

 

6. Concentric loops but their planes are at an angle ϴ with each other-

B_{net}=\sqrt{{B_{1}}^2+{B_2}^2+2B_1B_2\cos\theta }

 

 

 

 

 

 

 

 

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Magnetic Field due to circular current loop

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