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:
1. \(\frac{\mu_0i}{R}\)
2. \(\frac{\mu_0i}{2R}\)
3. \(\frac{2\mu_0i}{R}\)
4. \(\frac{3\mu_0i}{8R}\)

Subtopic:  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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The magnetic induction at point \(P\), which is \(4\) cm from a long current-carrying wire is \(10^{-8}\) Tesla. What would be the field of induction at a distance of \(12\) cm from the same current?
1. \(3.33\times 10^{-9}\) Tesla   
2. \(1.11\times 10^{-4}\) Tesla
3. \(3\times 10^{-3}\) Tesla
4. \(9\times 10^{-2}\) Tesla
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Two straight horizontal parallel wires carry the same current in the same direction, and \(d\) is the distance between them. You are given a small magnetic needle that is freely suspended. Which of the following positions will have the needle's orientation independent of the magnitude of the current in the wires?
1. At a distance \(\frac{d}{2}\) from any of the wires in any plane.
2. At a distance \(\frac{d}{3}\) from any of the wires in the horizontal plane.
3. Anywhere on the circumference of a vertical circle of radius \(d\) and centre halfway between the wires.
4. 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 

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. \(B =\frac{4 \pi}{\mu_0} \frac{r}{2 i}\)

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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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