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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. 1/r
2. 1/r^3/2
3. 1/r²
4. 1/r³

The magnetic field due to a straight conductor of uniform cross-section of radius a and carrying a steady current is represented by :
1. 
2. 
3. 
4. 

Two parallel beams of positrons moving in the same direction will :
1. repel each other
2. will not interact with each other
3. attract each other
4. be deflected normal to the plane containing the two beams

A proton and an $\mathrm{\alpha }$-particle, moving with the same velocity, enter a uniform magnetic field, acting normal to the plane of their motion. The ratio of the radii of the circular paths described by the proton and $\mathrm{\alpha }$-particle is :
1. 1:2
2. 1:4
3. 4:1
4. 1:16

Circular loop of a wire and a long straight wire carry currents I_c and I_e, respectively as shown in figure. Assuming that these are placed in the same plane, the magnetic fields will be zero at the centre of the loop when the separation H is :

1. $\frac{{\mathrm{I}}_{\mathrm{e}}\mathrm{R}}{{\mathrm{I}}_{\mathrm{c}}\mathrm{\pi }}$
2. $\frac{{\mathrm{I}}_c\mathrm{R}}{{\mathrm{I}}_e\mathrm{\pi }}$
3. $\frac{{\mathrm{\pi I}}_{\mathrm{c}}}{{\mathrm{I}}_{\mathrm{e}}\mathrm{R}}$
4. $\frac{{\mathrm{I}}_{\mathrm{e}}\mathrm{\pi }}{{\mathrm{I}}_{\mathrm{c}}\mathrm{R}}$

What si the magnetic field at a distance R from a coil radius r carrying current I?
1. $\frac{{\mathrm{\mu }}_0{\mathrm{IR}}^2}{2{(\mathrm{R}}^{}}$² + r²)32
2. $\frac{{\mathrm{\mu }}_0{\mathrm{Ir}}^2}{2{(\mathrm{R}}^{}}$² + r²)32
3. $\frac{{\mathrm{\mu }}_0\mathrm{I}}{2\mathrm{r}}$
4. $\frac{{\mathrm{\mu }}_0\mathrm{l}}{2\mathrm{R}}$

A long straight wire of radius $\mathrm{\alpha }$ carries a steady current i. The current is uniformaly distributed across its cross section. The ratio of the magnetic field at a/2 and 2a is
1. 1/2
2. 1/4
3. 4
4. 1

In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential V and then made to decribe semicircular paths of radius R using a magnetic field B. If V and B are kept constant, the ratio $\left(\frac{\mathrm{charge} \mathrm{on} \mathrm{the} \mathrm{ion}}{\mathrm{mass} \mathrm{of} \mathrm{the} \mathrm{ion}}\right)$ will be proportional to
1. $\frac{1}{\mathrm{R}}$
2. $\frac{1}{{\mathrm{R}}^2}$
3. ${\mathrm{R}}^2$
4. R

Two concentric coils each of radius equal to 2 $\mathrm{\pi }$ cm are placed at right angles to each other. 3 ampere and 4 ampere are the currents flowing in each coil respectively. The magnetic induction in Weber/${\mathrm{m}}^2$ at the centre of the coils will be $({\mathrm{\mu }}_0 = 4\mathrm{\pi } \mathrm{x} {10}^{-7} \mathrm{Wb}/\mathrm{A}.\mathrm{m})$
1. ${10}^{-5}$
2. $12 \mathrm{x} {10}^{-5}$
3. $7 \mathrm{x} {10}^{-5}$
4. $5 \mathrm{x} {10}^{-5}$

The magnetic field due to a square loop of side a carrying a current I at its centre is
1. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{2\mathrm{a}}$
2. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{\sqrt{2}\mathrm{\pi a}}$
3. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{2\mathrm{\pi a}}$
4. $\sqrt{2}\frac{{\mathrm{\mu }}_0\mathrm{i}}{\mathrm{\pi a}}$

Electron of mass m and charge q is travelling with a speed along a circular path of radius r at right angles to a uniform magnetic field of intensity B. If the speed of the electron is doubled anf the magnetic field is halved the resulting path would have a radius
1. 2r
2. 4r
3. $\frac{\mathrm{r}}{4}$ 
4. $\frac{\mathrm{r}}{2}$

Electron moves at right angles to a magnetic field of 1.5 x 10${}^{-2}$ tesla with speed of 6 x 10${}^7$ m/s. If the specific charge of the electron is 1.7 x 10${}^{11}$ C/kg. The radius of circular path will be
1. 3.31 cm
2. 4.31 cm
3. 1.31 cm
4. 2.35 cm

An electron beam passes through a magnetic field of 2 x 10${}^{-3}$ Wb/m${}^2$ and an electric field of 1.0 x 10${}^4$ V/m both acting simultaneously. The path of electron remains undeviated. The speed of electron if the electric field is removed, and the radius of electron path will be respectively
1. 10 x 10${}^6$ m/s, 2.43 cm
2. 2.5 x 10${}^6$ m/s, 0.43 cm
3. 5 x 10${}^6$ m/s, 1.43 cm
4. none of these

A charged particle is released from rest in a region of uniform electric and magnetic fields that are parallel to each other. The particle will move on a:
1. straight line
2. circle
3. helix
4. cycloid

Four wires, each of length 2.0 m, are bent into four loops P, Q, R and S and then suspended in a uniform magnetic field. if the same current is passed each other, then the torque will be maximum on the loop

1. P 
2. Q
3. R
4. S

A square coil of side a carries a current I. The magnetic field at the centre of the coil is

1. $\frac{{\mathrm{\mu }}_{\mathrm{o}}\mathrm{I}}{\mathrm{a\pi }}$
2. $\frac{\sqrt{2}{\mathrm{\mu }}_0\mathrm{I}}{\mathrm{a\pi }}$
3. $\frac{{\mathrm{\mu }}_0\mathrm{I}}{\sqrt{2}\mathrm{a\pi }}$
4. $\frac{2\sqrt{2}{\mathrm{\mu }}_0\mathrm{I}}{\mathrm{a\pi }}$

A charged particle moves through a magnetic field in a direction perpendicular to it. Then the 

Wires 1 and 2 carrying currents ${\mathrm{i}}_1$ and ${\mathrm{i}}_2$ respectively are inclined at an angle $\mathrm{\theta }$ to each other. What is the force on a small element d/ of wire 2 at a distance of r wire 1 (as shown in figure) due to the magnetic field of wire 1?

1. $\frac{{\mathrm{\mu }}_0}{2\mathrm{\pi r}}{i}_1{i}_2 dl \tan \theta$
2. $\frac{{\mathrm{\mu }}_0}{2\mathrm{\pi r}}{i}_1{i}_2 dl \sin \theta$
3. $\frac{{\mathrm{\mu }}_0}{2\mathrm{\pi r}}{i}_1{i}_2 dl \cos \theta$
4. $\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi r}}{i}_1{i}_2 dl \sin \theta$
 

If we double the radius of a coil keeping the current through it unchanged, then the magnetic field at any point at a large distance from the centre becomes approximately
1. double
2. three times
3. four times
4. one-fourth

A portion of a conductive wire is bent in the form of a semicircle of radius r as shown nelow in fig. At the centre of semicircle, the magnetic induction will be

1. zero
2. infinite
3. $\frac{{\mathrm{\mu }}_0}{4 \mathrm{\pi }}.\frac{\mathrm{\pi i}}{r}gauss$
4. $\frac{{\mathrm{\mu }}_0}{4 \mathrm{\pi }}.\frac{\mathrm{\pi i}}{r}\mathrm{tesla}$

A coil of circular cross-section having 1000 turns and 4 cm² face area is placed with its axis parallel to a magnetic field which decreases by 10^-2 Wb m^-2 in 0.01 s. The emf induced in the coil is :
1. 400 mV
2. 200 mV
3. 4 mV
4. 0.4 mV