Magnetic Field Due To Circular Current Loop MCQ - Practice Questions with Answers

Magnetic Field due to circular current loop at its centre: 

Magnetic Field due to circular coil at Centre-

$$B_0=B_{\text{Centre }}=\frac{{\mu }_0}{4\pi }\frac{2\pi Ni}{r}=\frac{{\mu }_{0}Ni}{2r}$$

where $\mathrm{N}=$ number of turns, $\mathrm{i}=$ current and $\mathrm{r}=$ radius of a circular coil.
Similarly, if Arc subtend angle theta at the centre as shown below then

$$B_0=\frac{{\mu }_0}{4\pi }\cdot \frac{\theta i}{r}$$
 

 

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

$$B_0=\frac{{\mu }_0}{4\pi }\cdot \frac{(2\pi -\theta )i}{r}$$
 

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 is 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 diameterthen $B_0=0$

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-

 

  

$$B_{\text{centre }}=\frac{{\mu }_o}{4\pi }2\pi i[\frac{1}{r_1}+\frac{1}{r_2}]$$

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

$$B_{\text{centre }}=\frac{{\mu }_o}{4\pi }2\pi i[\frac{n_1}{r_1}+\frac{n_2}{r_2}]$$
 

 

 

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

 

$$B_{\text{centre }}=\frac{{\mu }_o}{4\pi }2\pi i[\frac{1}{r_1}-\frac{1}{r_2}]$$

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

$$B_{\text{centre }}=\frac{{\mu }_o}{4\pi }2\pi i[\frac{n_1}{r_1}-\frac{n_2}{r_2}]$$
 

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

Then $B_{\text{net }}=\sqrt{B_1^2+B_2^2}$

 

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

$B_{\text{net }}=\sqrt{B_1^2+B_2^2+2B_1{B}_2\cos \theta }$