A wire in the form of a square of side ‘a’ carries a current i. Then the magnetic induction at the centre of the square wire is (Magnetic permeability of free space = ${\mathrm{\mu }}_{0}$)

1. $\frac{{\mathrm{\mu }}_{0}\mathrm{i}}{2\mathrm{\pi a}}$                   2.  $\frac{{\mathrm{\mu }}_{0}\mathrm{i}\sqrt{2}}{\mathrm{\pi a}}$

3.               4.  $\frac{{\mathrm{\mu }}_{0}\mathrm{i}}{\sqrt{2}\mathrm{\pi a}}$

Concept Questions :-

Magnetic field due to various cases
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An electron moving in a circular orbit of radius r makes n rotation per second. The magnetic field produced at the centre has a magnitude of :

(a)  $\frac{{\mathrm{\mu }}_{0}\mathrm{ne}}{2\mathrm{r}}$                                     (b)  $\frac{{\mathrm{\mu }}_{0}{\mathrm{n}}^{2}\mathrm{e}}{2\mathrm{r}}$

(c)  $\frac{{\mathrm{\mu }}_{0}\mathrm{ne}}{2\mathrm{\pi r}}$                                      (d)  Zero

Concept Questions :-

Magnetic field due to various cases
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Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describes circular path of radius ${\mathrm{R}}_{1}$ and ${\mathrm{R}}_{2}$ respectively. The ratio of mass of X to that of Y is :

(a)  ${\left(\frac{{\mathrm{R}}_{1}}{{\mathrm{R}}_{2}}\right)}^{1/2}$                         (b)  $\frac{{\mathrm{R}}_{2}}{{\mathrm{R}}_{1}}$

(c)  ${\left(\frac{{\mathrm{R}}_{1}}{{\mathrm{R}}_{2}}\right)}^{2}$                             (d)  $\frac{{\mathrm{R}}_{1}}{{\mathrm{R}}_{2}}$

Concept Questions :-

Lorentz force
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A beam of ions with velocity  enters normally into a uniform magnetic field of $4×{10}^{-2}$tesla. If the specific charge of the ion is $5×{10}^{7}$ C/kg , then the radius of the circular path described will be :

(a) 0.10 m              (b)  0.16 m

(c)  0.20 m              (d) 0.25 m

Concept Questions :-

Lorentz force
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If the direction of the initial velocity of the charged particle is perpendicular to the magnetic field, then the orbit will be
or
The path executed by a charged particle whose motion is perpendicular to magnetic field is :

(a) A straight line                                (b) An ellipse
(c) A circle                                          (d) A helix

Concept Questions :-

Lorentz force
Please attempt this question first.

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A proton and an $\mathrm{\alpha }-$ particle enter a uniform magnetic field perpendicularly with the same speed. If proton takes 25 $\mathrm{\mu }$ sec to make 5 revolutions, then the periodic time for the $\mathrm{\alpha }-$particle would be :

(a) 50 $\mathrm{\mu }$ sec                (b) 25 $\mathrm{\mu }$ sec

(c) 10 $\mathrm{\mu }$ sec                 (d) 5 $\mathrm{\mu }$ sec

Concept Questions :-

Lorentz force
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An $\mathrm{\alpha }-$ particle travels in a circular path of radius 0.45 m in a magnetic field  with a speed of  . The period of revolution of the $\mathrm{\alpha }-$ particle is :

(a)   sec          (b)  $1.1×{10}^{-6}$ sec

(c)  $1.1×{10}^{-7}$ sec           (d)  $1.1×{10}^{-8}$ sec

Concept Questions :-

Lorentz force
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A deutron of kinetic energy 50 keV is describing a circular orbit of radius 0.5 metre in a plane perpendicular to magnetic field $\stackrel{\to }{\mathrm{B}}$. The kinetic energy of the proton that describes a circular orbit of radius 0.5 metre in the same plane with the same $\stackrel{\to }{\mathrm{B}}$ is :

(a) 25 kev                           (b) 50 kev

(c) 200 kev                          (d) 100 kev

Concept Questions :-

Lorentz force
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A rectangular loop carrying a current i is situated near a long straight wire such that the wire is parallel to the one of the sides of the loop and is in the plane of the loop. If a steady current I is established in wire as shown in figure, the loop will

(a) Rotate about an axis parallel to the wire

(b) Move away from the wire or towards right

(c) Move towards the wire

(d) Remain stationary

Concept Questions :-

Current carrying loop : Force and torque
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Two thin long parallel wires separated by a distance b are carrying a current i amp each. The magnitude of the force per unit length exerted by one wire on the other is

(a) $\frac{{\mu }_{0}{i}^{2}}{{b}^{2}}$                                  (b) $\frac{{\mu }_{0}{i}^{2}}{2\mathrm{\pi b}}$

(c) $\frac{{\mu }_{0}i}{2\mathrm{\pi b}}$                                   (d) $\frac{{\mu }_{0}i}{2{\mathrm{\pi b}}^{2}}$

Concept Questions :-

Force between current carrying wires
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