Magnetism and Matter Test 44

Result

Magnetism and Matter Test 44

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

In a given figure an isosceles triangle conducting wire is entering into the region of perpendicular uniform magnetic field $$B_0$$ with constant velocity $$V_0$$. The magnitude of induced emf as a function of time(t) in the wire is(till side is outside the field)

A
$$B_0V^2_0t^2$$

B
$$2B_0V^2_0t^2$$

C
$$2B_0V^2_0t$$

D
$$2B_0V_0t$$

Solution
Question 2
1 / -0

A conducting ring of radius $$1$$ metre is placed in a uniform magnetic field $$B$$ of $$0.01$$ tesla oscillating with frequency $$100Hz$$ with its plane at right angle to $$B$$. What will be the maximum induced electric field?

A
$$\pi$$ volt/m

B
$$2$$ volt/m

C
$$10$$ volt/m

D
$$62$$ volt/m
Question 3
1 / -0

Three magnets of the same length but moments M, $$2$$M and $$3$$M are arranged in the forms of an equilateral triangle with opposite pole nearer, the resultant magnetic moment of the arrangement is?

A
$$6$$M

B
Zero

C
$$\sqrt{3}$$M

D
$$\dfrac{\sqrt{3}}{2}$$M

Solution

$$\vec M=(M-2M\cos 60-3M \cos 60)\hat i+(2M\cos 30-3M\cos 30)$$
$$\vec M=\dfrac {-3}{2}M\hat i-\dfrac {\sqrt 3}{2}M$$
$$M=|\vec M|=\sqrt {\left (\dfrac {3}{2}\right)^2 +\left (\dfrac {\sqrt 3}{2}\right)^2}M=\sqrt 3 M$$
Magnetic moment $$=\sqrt 3M$$
Question 4
1 / -0

A thin conducting rod of length $$l$$ is moved such that its end $$B$$ moves along the X-axis while end $$A$$ moves along the Y-axis. A uniform magnetic field $$B = {B_0}\hat k$$ exists in the region. At some instant, the velocity of end $$B$$ is $$v$$ and the rod makes an angle of $$\theta = 60$$ with the X-axis as shown in the figure. Then, at this instant

A
angular speed of rod $$AB$$ is $$\omega = \dfrac{{2v}}{{\sqrt 3 l}}$$

B
angular speed of rod $$AB$$ is $$\omega = \dfrac{{\sqrt 3 v}}{{2l}}$$

C
e.m.f. induced in rod $$AB$$ is $$Blv\sqrt 3 $$

D
e.m.f. induced in rod $$AB$$ is $$Blv/2\sqrt 3 $$

Solution

$$\begin{array}{l}OB = x = l\cos \theta \\\dfrac{{dx}}{{dt}} = - l\sin \theta \left( {\dfrac{{d\theta }}{{dt}}} \right)\\\dfrac{{d\theta }}{{dt}} = - \dfrac{1}{{l\sin \theta }}\left( {\dfrac{{dx}}{{dt}}} \right)\\ \Rightarrow \omega = - \dfrac{1}{{l\sin \theta }} \times {v_B}\\ \Rightarrow \omega = - \dfrac{1}{{l\sin 60}} \times v\\ \Rightarrow \omega = - \dfrac{v}{{l \times \sqrt 3 /2}} = \dfrac{{ - 2v}}{{\sqrt 3 l}}\\so,\omega = \dfrac{{2v}}{{\sqrt 3 l}}\end{array}$$
Question 5
1 / -0

At a place earth's magnetic field, $$5\times 10^{-5}\,Wb/m^2$$ is acting perpendicular to a coil of radius R=5 cm. If $$\dfrac{\mu_0}{4\pi}=10^{-7}$$, then how much current is induced in circular loop?

A
0.2 A

B
0 A

C
4 A

D
40 A

Solution
Question 6
1 / -0

A coil having $$n$$ turns and resistance $$4R$$ $$ \Omega$$. This combination is moved in time $$t$$ seconds from a magnetic field $$W_1$$ weber to $$W_2$$ weber. The induced current in the circuit is :

A
$$-\dfrac{W_2-W_1}{5Rnt}$$

B
$$-\dfrac{(W_2-W_1)}{5Rnt}$$

C
$$\dfrac{W_2-W_1}{Rnt}$$

D
$$\dfrac{n(W_2-W_1)}{5Rt}$$
Question 7
1 / -0

A ferromagnetic material is placed in an external magnetic field. The magnetic domains

A
Increase in size

B
Decrease in size

C
May increase or decrease is size

D
Have no relation with the field

Solution

The magnetic domain align themselves in the direction of the external magnetic field, for a ferromagnetic substance.
Refer image,
Domains are basically small neighborhoods of atoms having direction. When kept in an external magnetic field, the domains aligned with the field expand take over regions previously occupied by domains aligned opposite to the field.
Hence, option (A) is correct
i.e Domains increases in rise.
Question 8
1 / -0

Two concentric circular loops of radii $$R$$ and $$2R$$ carry currents of $$2i$$ and $$i$$ respectively in opposite sense (ie. Clockwise in one coil and center clockwise in the other oil). The resultant magnetic field at their common center is

A
$$\mu _{0}\dfrac {i}{4R}$$

B
$$\mu _{0}\dfrac {5i}{4R}$$

C
$$\mu _{0}\dfrac {3i}{4R}$$

D
`$$\mu _{0}\dfrac {i}{2R}$$

Solution
Question 9
1 / -0

A electron moves in a circular orbit at a distance from a proton with kinetic energy E. to escape to infinity, the energy which must be supplied to the electron is:

A
E

B
$$2E$$

C
$$0.5E$$

D
$$\sqrt2E$$

Solution
Question 10
1 / -0

A bar magnet freely suspended in a vibration magnetometer has time period T at a place A and T/2 at a place B. If horizontal component of earth's magnetic field at A is $$36 \times 10^{-6}$$ T, then its value at 'B' is

A
$$100 \times 10^{-6}$$

B
$$72 \times 10^{-6}$$

C
$$144 \times 10^{-6}$$

D
None

Solution