Two wires of large length carry equal currents each i. One wire is kept along x-axis and the other is kept along y-axis. The magnitude of magnetic field at a point on z-axis at distance d from the origin is

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

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

3. $\frac{{\mu }_{0}i}{\mathrm{\pi d}}$

4. zero

To compensate the relativistic variation of mass at high speed of charge in cyclotron. Adjustments can be made is :

1. Frequency of a.c is decreased 

2. Magnetic field is increased 

3. Peak value of a.c is increased 

4. Both (1) & (2)

A infinite straight wire carrying current 3 A and other carrying 6 A in the same direction produce a magnetic field of 12 tesla at the midpoint of the line joining them. When 6-ampere current wire is switched off, the magnetic field will be :

1. 24 T

2. 3 T

3. 6 T

4. 12 T

The magnetic field at origin in the situation shown in the figure has magnitude (BCD is a semi-circular arc of radius R in xz plane) 

1. $\frac{{\mu }_{0}l}{4\mathrm{\pi R}}$

2. $\frac{{\mu }_{0}l}{2\mathrm{\pi R}}\sqrt{4+{\mathrm{\pi }}^2}$

3. $\frac{{\mu }_{0}l}{2\mathrm{\pi R}}\sqrt{R^2+{\mathrm{\pi }}^2}$

4. $\frac{{\mu }_{0}l}{4\mathrm{\pi R}}\sqrt{1+{\mathrm{\pi }}^2}$

Three long straight wires A, B, and C are shown in figure. The resultant magnetic force on wire B is 

1. Towards left

2. Towards right

3. Upwards (perpendicular to the plane of paper)

4. Downwards (perpendicular to the plane of paper)

In a moving coil galvanometer the deflection $\theta$ of the coil is related to the electric current by the relation

1. $l\propto \tan \theta$

2. $l\propto \cos \theta$

3. $l\propto \theta$

4. $l\propto {\theta }^2$

A half-metre long wire is lying in a plane perpendicular to the magnetic field. A force of 2 kg wt is acting on it in a magnetic field of 0.98 tesla. The current flowing in it will be

1. 400 A 

2. 40 A

3. 4 A

4. 1 A

A cyclotron cannot be used to accelerate 

1. Deutrons 

2. Protons 

3. Neutrons

4. Both (1) & (3)

                
1. \(\mu_{0} i_{1} i_{2}\)
2. \(\dfrac{\mu_{0} i_{1} i_{2}}{\pi}\)
3. \(\dfrac{\mu_{0} i_{1} i_{2}}{2 \pi}\)
4. \(2 \mu_{0} i_{1} i_{2}\) 

Two long straight conductors with currents $l_1 and l_2$ are placed along X and Y-axes. The locus of points of zero magnetic induction is

1. A parabola

2. A rectangular hyperbola

3. A straight line

4. An ellipse