A current i ampere flows in a circular arc of wire whose radius is R, which subtend an angle 3π2 radian at its centre. The magnetic induction B at the centre is :

(a) μ0iR

(b) μ0i2R

(c)2μ0iR

(d) 3μ0i8R 

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Magnetic field due to various cases
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A straight section PQ of a circuit lies along the X-axis from x=-a2 to x= a2 and carries a steady current i. The magnetic field due to the section PQ at a point X = + a will be:


1. Proportional to a             2. Proportional to a2
3. Proportional to 1a           4. Zero

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Magnetic field due to various cases
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The magnetic induction at a point P which is distant 4 cm from a long current carrying wire is 10-8 Tesla . The field of induction at a distance 12 cm from the same current would be :
(a)   3.33×10-9 Tesla                            

(b) 1.11×10-4 Tesla
(c)    3×10-3     Tesla

(d)  9×10-2    Tesla

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Magnetic field due to various cases
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Two straight horizontal parallel wires are carrying the same current in the same direction, d is the distance between the wires. You are provided with a small freely suspended magnetic needle. At which of the following positions will the orientation of the needle be independent of the magnitude of the current in the wires:

 

(a) At a distance d/2 from any of the wires in any plane

(b) At a distance d/2 from any of the wires in the horizontal plane

(c) Anywhere on the circumference of a vertical circle of radius d and centre halfway between the wires

(d) At points halfway between the wires in the horizontal plane

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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 

(a) 1r                                           (b) 1r3/2
(c) 1r2                                           (d) 1r3 

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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

(a) B=μ04π2ir                                                 (b) B=μ04πr2i
(c)  B=4πμ02ir                                                 (d) B=4πμ0r2i

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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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Magnetic field due to various cases
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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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Magnetic field due to various cases
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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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Magnetic field due to various cases
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 In the figure shown there are two semicircles of radii r1 and r2 in which a current i is flowing. The magnetic induction at the centre O will be :

(a)  μ0irr1+r2                           

(b)  μ0i4r1+r2r1r2

(c)  μ0i4(r1-r2)                             

(d) μ0i4r2-r1r1r2  

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Magnetic field due to various cases
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