Moving Charges and Magnetism Test

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Moving Charges and Magnetism Test - 44

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Weekly Quiz Competition

Question 1
1 / -0

The particles emitted by a radioactive substance are deflected in a magnetic field. The particle may be

A
neutrons

B
electrons

C
protons

D
hydrogen atoms

Solution

The particles not emitted by a radioactive substance are protons, hydrogen atoms are neutrons.
Question 2
1 / -0

A person is facing magnetic north. An electron in front of him flies horizontally towards the north and deflects towards east. He is in/at the

A
southern hemispheres.

B
the equator

C
northern hemispheres.

D
none of these

Solution

Now electron moves towards north and get deflected towards east therfore, vertical component of earth's magnetic field must be positive. Now when we find the direction of the force acting on electron by finding the direction of vector $$\overrightarrow { v } \times \overrightarrow { { B }_{ v } } $$
(We will neglect the horizontal component because it will be parallel to the direction of motion of electron hence $$\overrightarrow { v } \times \overrightarrow { { B }_{ H } }=0 $$).
The direction of this vector is towards west when $$B_v$$ is pointing downwards and our charge is electron therefore, force on it will exert in the direction of east.
Now vertical component is downward in southern hemisphere.
Question 3
1 / -0

Cathode rays are made to pass between the poles of a magnet. The effect of magnetic field is

A
to increase their velocity

B
to deflect them towards north pole

C
to deflect them towards south pole

D
to deflect them out of the plane of magnetic field

Solution

When a magnetic field is applied, the cathode ray is deflected from its normal straight path into a curved path which can be identified by right hand thumb rule.
Question 4
1 / -0

A charged particle of mass $$10^{-3}$$ kg and charge $$10^{-5}C$$ enters a magnetic field of induction 1 T. If $$g=10 ms^{-2}$$ for what value of velocity will it pass straight through the field without deflection?

A
$$10^{-3} ms^{-1}$$

B
$$10^{3} ms^{-1}$$

C
$$10^{6} ms^{-1}$$

D
$$1 ms^{-1}$$

Solution

Since the charged particle passes without being deflected,

$$F_{magnetic} = F_{gravity}$$

$$ \therefore qvB = mg$$

$$ \therefore v=\dfrac{mg}{qB}$$

$$=\dfrac{10^{-3} \times 10}{10 ^{-5} \times 1}=10^3\: m/s$$
Question 5
1 / -0

An electron is accelerated from rest through a potential difference $$V$$. This electron experiences of force $$F$$ in a uniform magnetic field. On increasing the potential difference to $$V^{'}$$, the force experienced by the electron in the same magnetic field becomes $$2F$$. Then, the ratio $$\dfrac{V^{'}}{V}$$ is equal to

A
$$\dfrac{4}{1}$$

B
$$\dfrac{2}{1}$$

C
$$\dfrac{1}{2}$$

D
$$\dfrac{1}{4}$$

Solution

$$K.E. = \dfrac{1}{2}mv^2 = eV$$

$$ \therefore v =\sqrt{\dfrac{2eV}{m}}$$

$$ F =eVB =e\sqrt{\dfrac{2eV}{m}}B$$

Given $$F' =2F = e\sqrt{\dfrac{2eV^{'}}{m}}B$$

$$\Rightarrow 2e\sqrt{\dfrac{2eV}{m}} B = e\sqrt{\dfrac{2eV'}{m}}B$$

$$ \Rightarrow V^{'} = 4V$$
Question 6
1 / -0

In a region of space, a uniform magnetic field $$B$$ exists in the $$x-$$direction. An electron is fired from the origin with its initial velocity $$u$$ making an angle $$\alpha$$ with the y direction in the $$yz$$ plane. In the subsequent motion of the electron,

A
$$y-$$coordinate of the electron will never be negative

B
$$z-$$coordinate of the electron will never be negative

C
$$x-$$coordinate of the electron will never be negative

D
trajectroy of the electron would be helical

Solution

The trajectory of the electron will lie in the $$yz$$ plane since magnetic field $$B$$ is $$\hat{i}$$ direction and initial velocity $$\overrightarrow{v}$$ is in $$yz$$ plane.
$$ \therefore x-$$coordinate of the electron will be zero always.
Question 7
1 / -0

A charged particle moves with velocity $$\vec v=a\hat i+d\hat j$$ in a magnetic field $$\vec B=A\hat i+D\hat j$$. The force acting on the particle has magnitude $$F$$. Then,

A
$$F=0$$, if $$aD=dA$$

B
$$F=0$$, if $$aD=-dA$$

C
$$F=0$$, if $$aA=-dD$$

D
$$F\propto (a^2+b^2)^{1/2}\times (A^2+D^2)^{1/2}$$

Solution

$$\vec{F} = q(\vec{v} \times \vec{B})$$

$$=q((a\hat{i} + d\hat{j} ) \times ( A\hat{i} + D\hat{j}))$$

$$=q( aD-dA)\hat{k}$$

If $$aD-dA=0$$

$$ \vec{F} =0$$
Question 8
1 / -0

A charged particle is whirled in a horizontal circle on a frictionless table by attaching it to a string fixed at one end. If a magnetic field is switched on in the vertical direction, the tension in the string

A
will increase.

B
will decrease.

C
remains same.

D
may increase or decrease.

Solution

Let the string makes an angle $$\theta$$ with the vertical.

Initially, before the magnetic field is applied, $$T \sin \theta= \dfrac{mv^2}{r}$$

If the particle experiences a force outward in the direction of the radius, tension $$T$$ will increase.
If the particle experiences a force inward in the direction of the radius towards the center, tension $$T$$ will decrease.
Question 9
1 / -0

A particle of specific charge $$\dfrac {q}{m}=\pi \ C kg^{-1}$$ is projected from the origin toward positive $$x-$$axis with a velocity of $$10\ ms^{-1}$$ in a uniform magnetic field $$\overrightarrow{B}=-2\hat{k} T$$. The velocity $$\overrightarrow{v}$$ of particle after time $$t=\dfrac{1}{12}\ s$$ will be $$($$in $$ms^{-1})$$

A
$$5\left[\hat{i}+\sqrt 3\hat{j}\right]$$

B
$$5\left[\sqrt{3}\hat{i}+\hat{j}\right]$$

C
$$5\left[\sqrt 3\hat{ i}-\hat{ j}\right]$$

D
$$5\left[\hat{ i}+\hat{ j}\right]$$

Solution

Time period $$T=\dfrac{2 \pi m}{qB}=\dfrac{2 \pi}{\dfrac{q}{m}B}= \dfrac{2 \pi}{\pi \times 2}=1\:s$$

Since the particle will be at point $$P$$ after time $$t=\dfrac{1}{12}=\dfrac{T}{12}\: s$$ , it is deviated by an angle $$\theta= \dfrac{2\pi}{12}=30^0$$

Hence, velocity at point $$P$$

$$ \vec{v} = 10( \cos 30^0 \hat{i} + \sin 30^0 \hat{j})=10\left( \dfrac{\sqrt{3}}{2}\hat{i} + \dfrac{1}{2}\hat{j}\right)= 5(\sqrt{3}\hat{i} +1\hat{j})=5(\sqrt{3}\hat{i} +\hat{j})$$
Question 10
1 / -0

If a copper rod carries a direct current, the magnetic field associated with the current will be:

A
only inside the rod

B
only outside the rod

C
both inside and outside the rod

D
neither inside nor outside the rod

Solution

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Re-Attempt Weekly Quiz Competition

Moving Charges and Magnetism Test - 44

Result

Moving Charges and Magnetism Test - 44

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SHARING IS CARING

Question 1

neutrons

electrons

protons

hydrogen atoms

Solution

Question 2

southern hemispheres.

the equator

northern hemispheres.

none of these

Solution

Question 3

to increase their velocity

to deflect them towards north pole

to deflect them towards south pole

to deflect them out of the plane of magnetic field

Solution

Question 4

$$10^{-3} ms^{-1}$$

$$10^{3} ms^{-1}$$

$$10^{6} ms^{-1}$$

$$1 ms^{-1}$$

Solution

Question 5

$$\dfrac{4}{1}$$

$$\dfrac{2}{1}$$

$$\dfrac{1}{2}$$

$$\dfrac{1}{4}$$

Solution

Question 6

$$y-$$coordinate of the electron will never be negative

$$z-$$coordinate of the electron will never be negative

$$x-$$coordinate of the electron will never be negative

trajectroy of the electron would be helical

Solution

Question 7

$$F=0$$, if $$aD=dA$$

$$F=0$$, if $$aD=-dA$$

$$F=0$$, if $$aA=-dD$$

$$F\propto (a^2+b^2)^{1/2}\times (A^2+D^2)^{1/2}$$

Solution

Question 8

will increase.

will decrease.

remains same.

may increase or decrease.

Solution

Question 9

$$5\left[\hat{i}+\sqrt 3\hat{j}\right]$$

$$5\left[\sqrt{3}\hat{i}+\hat{j}\right]$$

$$5\left[\sqrt 3\hat{ i}-\hat{ j}\right]$$

$$5\left[\hat{ i}+\hat{ j}\right]$$

Solution

Question 10

only inside the rod

only outside the rod

both inside and outside the rod

neither inside nor outside the rod

Solution

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