1.
In the figure shown a coil of single turn is wound on a sphere of radius $$R$$ and mass $$M.$$ The plane of the coil is parallel to the plane and lies in the equatorial plane of the sphere. Current in the coil is $$i.$$ The value of $$B$$ if the sphere is in equilibrium is
A
$$\frac{{mg\cos \theta }}{{\pi iR}}$$
B
$$\frac{{mg}}{{\pi iR}}$$
C
$$\frac{{mg\tan \theta }}{{\pi iR}}$$
D
$$\frac{{mg\sin \theta }}{{\pi iR}}$$
Answer :
$$\frac{{mg}}{{\pi iR}}$$
2. A beam of cathode rays is subjected to crossed electric $$\left( E \right)$$ and magnetic fields $$\left( B \right).$$ The fields are adjusted such that the beam is not deflected. The specific charge of the cathode rays is given by
A
$$\frac{{{B^2}}}{{2V{E^2}}}$$
B
$$\frac{{2V{B^2}}}{{{E^2}}}$$
C
$$\frac{{2V{E^2}}}{{{B^2}}}$$
D
$$\frac{{{E^2}}}{{2V{B^2}}}$$
Answer :
$$\frac{{{E^2}}}{{2V{B^2}}}$$
3.
A rectangular loop of sides $$10 cm$$ and $$5 cm$$ carrying a current 1 of $$12\,A$$ is placed in different orientations as shown in the figures below :
If there is a uniform magnetic field of $$0.3 T$$ in the positive $$z$$ direction, in which orientations the loop would be in (i) stable equilibrium and (ii) unstable equilibrium?
A
(B) and (D), respectively
B
(B) and (C), respectively
C
(A) and (B), respectively
D
(A) and (C), respectively
Answer :
(B) and (D), respectively
4. A magnetic needle of magnetic moment $$6.7 \times {10^{ - 2}}A{m^2}$$ and moment of inertia $$7.5 \times {10^{ - 6}}kg\,{m^2}$$ is performing simple harmonic oscillations in a magnetic field of $$0.01 T.$$ Time taken for 10 complete oscillations is :
A
$$6.98 s$$
B
$$8.76 s$$
C
$$6.65 s$$
D
$$8.89 s$$
Answer :
$$6.65 s$$
5.
The figure shows two long straight current carrying wire separated by a fixed distance $$d.$$ The magnitude of current, flowing in each wire varies with time but the magnitude of current in each wire is equal at all times.
Which of the following graphs shows the correct variation of force per unit length $$f$$ between the two wires with current $$i$$ ?
A
B
C
D
Answer :
6. A milli voltmeter of 25 milli volt range is to be converted into an ammeter of 25 ampere range. The value (in $$ohm$$ ) of necessary shunt will be
A
0.001
B
0.01
C
1
D
0.05
Answer :
0.001
7. A current loop in a magnetic field
A
experiences a torque whether the field is uniform or non-uniform in all orientations
B
can be in equilibrium in one orientation
C
can be in equilibrium in two orientations, both the equilibrium states are unstable
D
can be in equilibrium in two orientations, one stable while other is unstable
Answer :
can be in equilibrium in two orientations, one stable while other is unstable
8. A moving coil galvanometer has a resistance of $$900\,\Omega .$$ In order to send only $$10\% $$ of the main current through this galvanometer, the resistance of the required shunt is
A
$$0.9\,\Omega $$
B
$$100\,\Omega $$
C
$$405\,\Omega $$
D
$$90\,\Omega $$
Answer :
$$100\,\Omega $$
9.
A conducting loop carrying a current /is placed in a uniform
magnetic field pointing into the plane of the paper as shown. The loop will have a tendency to
A
contract
B
expand
C
move towards +ve $$x$$ -axis
D
move towards -ve $$x$$ -axis.
Answer :
expand
10. The magnetic field $$dB$$ due to a small element at a distance $$r$$ and carrying current $$i$$ is
A
$$dB = \frac{{{\mu _0}}}{{4\pi }}i\left( {\frac{{dl \times r}}{r}} \right)$$
B
$$dB = \frac{{{\mu _0}}}{{4\pi }}{i^2}\left( {\frac{{dl \times r}}{{{r^2}}}} \right)$$
C
$$dB = \frac{{{\mu _0}}}{{4\pi }}{i^2}\left( {\frac{{dl \times r}}{r}} \right)$$
D
$$dB = \frac{{{\mu _0}}}{{4\pi }}i\left( {\frac{{dl \times r}}{{{r^3}}}} \right)$$
Answer :
$$dB = \frac{{{\mu _0}}}{{4\pi }}i\left( {\frac{{dl \times r}}{{{r^3}}}} \right)$$
