A circular coil of radius R carries an electric current. The magnetic field due to the coil at a point on the axis of the coil located at a distance r from the centre of the coil, such that r >> R, varies as 

1. 1r                                          

2. 1r3/2

3. 1r2                                          

4. 1r3 

Subtopic:  Magnetic Field due to various cases |
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The magnetic induction due to an infinitely long straight wire carrying a current \(i\) at a distance \(r\) from the wire is given by:
1. \( B =\frac{\mu_0}{4 \pi} \frac{2 i}{r} \)
2. \(B =\frac{\mu_0}{4 \pi} \frac{r}{2 i} \)
3. \(B =\frac{4 \pi}{\mu_0} \frac{2 i}{r} \)
4. \(B =\frac{4 \pi}{\mu_0} \frac{r}{2 i}\)

Subtopic:  Magnetic Field due to various cases |
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The magnetic induction at the centre O in the figure shown is:                                                   

 1. μ0i41R1-1R2                                   2. μ0i41R1+1R2                                                         

 3. μ0i 4R1-R2                                      4. μ0i4R1+R2       

                        

 

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In the figure shown, the magnetic induction at the centre of the arc due to the current in portion AB will be

(a) μ0ir                       (c)  μ0i4r

(b) μ0i2r                        (d) Zero

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Two concentric circular coils of ten turns each are situated in the same plane. Their radii are 20 and 40 cm and they carry respectively 0.2 and 0.3 ampere current in opposite direction. The magnetic field in weber/m2 at the centre is :

(a) 354μ0                              (b) μ080
(c)  780μ0                              (d) 54μ0

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In the figure shown below there are two semicircles of radius \(r_1\) and \(r_2\) in which a current \(i\) is flowing. The magnetic induction at the centre of \(O\) will be:


 

1. \(\dfrac{\mu_{0} i}{r} \left(r_{1} + r_{2}\right)\) 2. \(\dfrac{\mu_{0} i}{4} \left[\frac{r_{1} + r_{2}}{r_{1} r_{2}}\right]\)
3. \(\dfrac{\mu_{0} i}{4} \left(r_{1} - r_{2}\right)\) 4. \(\dfrac{\mu_{0} i}{4} \left[\frac{r_{2} - r_{1}}{r_{1} r_{2}}\right]\)
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The direction of magnetic lines of forces close to a straight conductor carrying current will be:

(1) along the length of the conductor.

(2) radially outward.

(3) circular in a plane perpendicular to the conductor.

(4) helical.

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A vertical wire kept in Z-X plane carries a current from Q to P (see figure). The magnetic field due to current-carrying wire will have the direction at the origin O along :

(1) OX

(2) OX'

(3) OY

(4) OY'

 


                                                                           

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 The magnetic field at the centre of a coil of n turns, bent in the form of a square of side 2 l, carrying current i, is :

(a)  2μ0niπl                               (b)  2μ0ni2πl

(c)  2μ0ni4πl                                (d)  2μ0niπl

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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 a radius \(2R\) and if \(2I\) is the current flowing through it, then the magnetic fields at the centre of the circular coil are in the ratio of (i.e. BA to BB):
1. \(4:1\)                             
2. \(2:1\)
3. \(3:1\)                             
4. \(1:1\)

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