Moving Charges & Magnetism + Magnetism and Matter

A metallic rod of mass per unit length 0.5 kg m^-1 is lying horizontally on a smooth inclined plane which makes an angle of 30° with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induction 0.25 T is acting on it in the vertical direction. The current flowing in the rod to keep stationery is:
1. 7.14 A
2. 5.98 A
3. 14.76 A
4. 11.32 A

A long straight wire of radius a ' carries a steady current I. The current is uniformly distributed over its cross-section. The ratio of the magnetic fields B and B' at radial distances

\frac{a}{2}

and 2a respectively, from the axis of the wire, is:
1.

\frac{1}{2}

2. 1
3. 4
4.

\frac{1}{4}

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 describe semi-circular paths of radius R using a magnetic field B. If V and B are kept constant, the ratio $\frac{C h a r g e o n t h e i o n}{m a s s o f t h e i o n}$ , will be proportional to:
1. $\frac{1}{R}$
2. $\frac{1}{R^{2}}$
3. $R^{2}$
4. R

A galvanometer of resistance 50

Ω

is connected to a battery of 3 V along with a resistance of 2950 Ω in series. A full-scale deflection of 30 divisions is obtained in the galvanometer. In order to reduce its deflection to 20 divisions, the resistance in series should be:

1. 5050 Ω
2. 5550 Ω
3. 6050 Ω
4. 4450 Ω

Force between two identical bar magnets whose centres are r metre apart is 4.8 N, when their axes are in the same line. If separation is increased to 2r, the force between them is reduced to
1. 2.4N 2. 1.2N
3. 0.6N 4. 0.3N

A bar magnet having a magnetic moment of 2 x 10⁴ JT^-1 is free to rotate in a horizontal plane. A horizontal magnetic field B = 6 x 10^-4T exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction 60 ° from the field is
1. 0.6 J
2. 12 J
3. 6 J
4. 2 J

A bar magnet of length ‘l’ and magnetic dipole moment ‘M’ is bent in the form of an arc as shown in figure. The new magnetic dipole moment will be:

1. 3M/

π

2. 2M/l

π

3. M/2
4. M

If $ϕ_{1}$ and $ϕ_{2}$ be the angles of dip observed in two vertical planes at right angles to each other and $ϕ$ be the true angle of dip, then
1. $\cos^{2} ϕ = \cos^{2} ϕ_{1} + \cos^{2} ϕ_{2}$
2. $\sec^{2} ϕ = \sec^{2} ϕ_{1} + \sec^{2} ϕ_{2}$
3. $\tan^{2} ϕ = \tan^{2} ϕ_{1} + \tan^{2} ϕ_{2}$
4. $\cot^{2} ϕ = \cot^{2} ϕ_{1} + \cot^{2} ϕ_{2}$

The variation of magnetic susceptibility $(χ)$ with temperature for a diamagnetic substance is best represented by
1.
2.
3.
4.

10.

Electromagnets are made of soft iron because soft iron has
1. low retentivity and high coercive force
2. high retentivity and high coercive force
3. low retentivity and low coercive force
4. high retentivity and low coercive force

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