Magnetic Effects of Current and Magnetism Test

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Magnetic Effects of Current and Magnetism Test - 6

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Question 1
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Directions: The following question has four choices out of which only one is correct.

A bar magnet of length 3 cm has points A and B along its axis at distances of 24 cm and 48 cm, respectively, on the opposite sides.

Ratio of the magnitudes of the magnetic fields at these points will be

A
8 : 1

B
1 : 2

C
3 : 1

D
4 : 1

Solution
Question 2
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The effective length of a magnet is 31.4 cm and its pole strength is 0.5 A-m. What will be the magnetic moment if it is bent in the form of a semicircle?

A
0.1 A-m²

B
0.01 A-m²

C
0.2 A-m²

D
1.2 A-m²

Solution

If L is length of the magnet, then magnetic moment, M = mL (where m is the pole strength).
When same magnet is bent into a semicircle of radius r, then
Separation between the poles = 2r
New magnetic moment of the bar magnet is:
Question 3
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A magnet of magnetic moment 20 CGS units is freely suspended in a uniform magnetic field of intensity 0.3 CGS units. The amount of work done in deflecting it by an angle of 30° (in CGS units) is

A
6

B
3

C
3 (2 - )

D
3

Solution
Question 4
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A steel wire of length 'l' has a magnetic moment M. It is bent into a semicircular arc. The new magnetic moment is

A
M

B
2M/π

C
M/π

D
Mπ

Solution

If m is pole strength, then m =
When the wire is bent into a semicircular arc, the separation between the two poles changes from l to 2r, where r is radius of the semicircular arc.

Since l = π r or r = l/π, the new magnetic moment of the stell wire,

M' = m × 2r =
Question 5
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At a point on the axial line of a bar magnet of dipole moment M, the magnetic potential is V. What is the magnetic potential due to a bar magnet of dipole moment M/4 at the same point?

A
4V

B
2V

C
V/2

D
V/4

Solution
Question 6
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Directions: For the statements of Assertion and Reason, mark the correct answer.

(a) If both assertion and reason are true and reason is the correct explanation of assertion.
(b) If both assertion and reason are true, but reason is not the correct explanation of assertion.
(c) If assertion is true, but reason is false.
(d) If both assertion and reason are false.

Assertion: A disc-shaped magnet levitates above a superconducting material that has been cooled by liquid nitrogen.
Reason: Superconductors repel a magnet.

A
(a)

B
(b)

C
(c)

D
(d)

Solution

Both assertion and reason are true and reason is the correct explanation of assertion.

A superconductor is a material that offers no electrical resistance and expels magnetic fields (Meissner effect) . All known superconductor materials exhibit superconducting properties when cooled to very low temperatures.
Question 7
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A loosely wound helix made of stiff wire is mounted vertically with the lower end just touching a dish of mercury. When a current from the battery is started in the coil through the mercury, then

A
the wire oscillates

B
the wire continues making contact

C
the wire breaks contact just when the current is passed

D
the mercury will expand by heating due to passage of current

Solution

When a current is passed through the helix, the neighbouring coils of the helix attract each other due to which it contracts. As a result, the contact is broken and the coils will recover their original states under the influence of a restoring force. The contact is made again and the process continues. Thus, the wire oscillates. Hence, the correct choice is (1).
Question 8
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A proton and an alpha particle enter a uniform magnetic field with the same velocity. The period of revolution of the alpha particle will be

A
four times that of the proton

B
two times that of the proton

C
three times that of the proton

D
five times that of the proton

Solution

The time period of the revolution in the magnetic field,

Mass of the alpha particle = 4 times the mass of the proton
Charge on the alpha particle = 2 times the charge on the proton
Question 9
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When an electron moves in a magnetic field in a direction perpendicular to the field, then its path will be

A
circular

B
elliptical

C
parabolic

D
helical

Solution

When an electron moves in a magnetic field in a direction perpendicular to the field, then its path will be circular as the force exerted by the magnetic field is perpendicular to both the magnetic field vector and the velocity vector. The necessary centripetal force is provided by the force due to the magnetic field.
Question 10
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An electron of mass m and charge q is travelling with a speed v along a circular path of radius r at a right angle to a uniform magnetic field of intensity B. If the speed of the electron is doubled and the intensity of magnetic field is halved, the resulting path would have a radius

A
2r

B
4r

C

D

Solution

(as r₁ = r)
Question 11
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The magnetic field due to a straight conductor of uniform cross-section of radius 'a' and carrying a steady current is represented by

A

B

C

D

Solution

For r < a; B ∝ r and for r > a, B ∝ 1/r.

Hence, option (1) is correct.
Question 12
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A wire PQR is bent as shown in the figure and is placed in a region of a uniform magnetic field B. The length of PQ = length of QR = L. A current l ampere flows through the wire as shown. The magnitude of the force on PQ and QR respectively will be

A
BIL and 0

B
2 BIL and 0

C
0 and BIL

D
0 and 0

Solution

A wire PQR is bent as shown in the figure and is placed in a region of a uniform magnetic field B. The length of PQ = length of QR = L. A current l ampere flows through the wire as shown. The magnitude of the force on PQ will be zero as the angle between the magnetic field and the current = 0.

Angle between the magnetic field and QR is 90°, so the force on QR,
Question 13
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A straight wire of mass 200 g and length 1.5 m carries a current of 2 A. It is suspended in mid-air by a uniform horizontal magnetic field B. The magnitude of B (in tesla) is (assume g = 9.8 ms^-2)

A
2

B
1.5

C
0.55

D
0.65

Solution

There is an upward force due to the magnetic field on current carrying which will balance the weight of the wire, if the wire is suspended in the mid air. So we have
Question 14
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A vertical straight conductor carries a current vertically upwards. A point P lies to the east of it, at a small distance and another point Q lies to the west of it, at the same distance. The magnetic field at P is

A
greater than that at Q

B
the same as that at Q

C
lesser than that at Q

D
greater or lesser than that at Q, depending upon the strength of the current

Solution

Let XY be a straight conductor carrying current i in the direction from X to Y. Magnetic field at P at a distance R is

Magnetic field will be same at both points P and Q because the distance of the points from current carrying wire is same. So, we can say that magnitude of the magnetic field is same on the both points.
Question 15
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A proton, a deuteron and an alpha particle, each having the same KE are moving in circular trajectories in a constant magnetic field. If the radii trajectories of these particles are r_p, r_d and r_a respectively, then

A
r_a= r_p< r_d

B
r_a > r_d > r_p

C
r_a = r_d < r_p

D
r_p = r_d=r_a

Solution

A proton, a deuteron and an alpha particle, each having the same KE are moving in circular trajectories in a constant magnetic field. The necessary centripetal force is provided by the force due to the magnetic field.

Kinetic energy of the particle is given by:

Radius of orbit,

Radius of the orbit for alpha particle,

Radius of the orbit for deutron,

Radius of the orbit of proton,