a A circular loop of radius a , carrying a current i , is placed in a two-dimensional magnetic field. The centre of the loop coincides with the centre of the field (figure). The strength of the magnetic field at the periphery of the loop is B . Find the magnetic force on the wire. b A hypothetical magnetic field existing in a region is given by B ⇀ = B 0 e ⇀ r , where e ⇀ r denotes the unit vector along the radial direction of a point relative to the origin and B 0 = constant. A circular loop of radius a , carrying a current i , is placed with its plane parallel to the X - Y plane and the centre at 0 , 0 , a . Find the magnitude of the magnetic force acting on the loop.

a Magnetic force is defined as the attractive or repulsive force that arises between electrically charged particles because of their motion. As a moving charged particle produces a magnetic field, similarly, magnetic fields also exert a certain force on moving charged particles. In the given case, the radius of the current-carrying loop is a , the current in the loop is i and the magnetic field acting on the loop is B . So force due to the magnetic field, F M → = i l → × B → ⇒ F M → = i l B sin θ n ^ Where, l → = length of the conductor. In this case, l → = 2 π a and since the magnetic field is always perpendicular to the length vector in the loop, θ = 90 ° . So, ⇒ F M → = i × 2 π a × B × sin 90 n ^ ⇒ F M → = 2 π a i B n ^ The direction of force due to the magnetic field can be known by using the right-hand thumb rule. By using before-mentioned rule, the direction of force due to the magnetic field is in the direction of the positive z -axis. ⇒ F M → = 2 π a i B k ^ . b In the given case, the current-carrying loop with current i and radius a , is placed parallel to X - Y plane at a perpendicular distance of a from the origin O , as shown in the diagram. So, F M → = i l B sin θ For this case, l = 2 π a and B → = B o e r → = B o a . Also, from the diagram, it can be known that sin θ = a 2 a = 1 2 . So, F M = i × 2 π a × B o a × 1 2 ⇒ F M = 2 π i a 2 B o 2 N ⇒ F M = π i a 2 B o 2 N .

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Two long wires carrying current in the same direction attract each other but two parallel beams of electrons moving in the same direction repel each other. Explain

Important Questions on Magnetic Effect of Current

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Alpha Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise - 1>Q 54

The magnetic field existing in a region is given by

\overset{⇀}{B} = B_{0} (1 - \frac{x}{l}) \hat{k}

, where

B_{0}

and

l

are constants,

x

is the

x -

coordinate of a point and

\hat{k}

is the unit vector along

z -

axis. A square loop of edge

l

and carrying a current

i

, is placed with its edges parallel to the

x, y

axis. Find the magnitude of the net magnetic force experienced by the loop.

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Alpha Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise - 1>Q 55

Figure shows a part of an electric circuit. The wires $AB, CD$ and $EF$ are very long and have identical resistances. The separation between the neighboring wires is $2 cm$ . The wires $AE$ and $BF$ have negligible resistance and the ammeter reads $60 A$ . Calculate the magnetic force per unit length on $AB$ and $CD$ .

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Alpha Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise - 1>Q 56

Two long straight parallel conductors are separated by a distance of

r_{1} = 5 cm

and carry constant currents

I_{1} = 10 A & I_{2} = 20 A

. What work per unit length of a conductor must be done to increase the separation between the conductors to

r_{2} = 10 cm

if, currents flow in the same direction?

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Alpha Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise - 1>Q 57

A straight wire of length $l$ can slide on two parallel plastic rails kept in a horizontal plane with a separation $d$ . The coefficient of friction between the wire and the rails is $μ .$ If the wire carries a current $i$ , what minimum magnetic field should exist in the space in order to slide the wire on the rails.

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Alpha Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise - 1>Q 58

A circular coil of

100

turns and having an effective radius of

0.05 m

carries a current of

0.1 A

. How much work is required to turn it in an external magnetic field of

1.5 Wb m^{- 2}

through

180 °

about an axis perpendicular to the magnetic field. The plane of the coil is initially perpendicular to the magnetic field

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Alpha Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise - 1>Q 59

$(a)$ A circular loop of radius $a$ , carrying a current $i$ , is placed in a two-dimensional magnetic field. The centre of the loop coincides with the centre of the field (figure). The strength of the magnetic field at the periphery of the loop is $B$ . Find the magnetic force on the wire.

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$(b)$ A hypothetical magnetic field existing in a region is given by $\overset{⇀}{B} = B_{0} {\overset{⇀}{e}}_{r}$ , where ${\overset{⇀}{e}}_{r}$ denotes the unit vector along the radial direction of a point relative to the origin and $B_{0} =$ constant. A circular loop of radius $a$ , carrying a current $i$ , is placed with its plane parallel to the $X - Y$ plane and the centre at $(0, 0, a)$ . Find the magnitude of the magnetic force acting on the loop.

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Alpha Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise - 1>Q 60

A rectangular coil of

100

turns has length

5 cm

and width

4 cm .

It is placed with its plane parallel to a uniform magnetic field and a current of

2 A

is sent through the coil. Find the magnitude of the magnetic field

B

, if the torque acting on the coil is

0.2 N m

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Alpha Question Bank for Engineering: Physics>Chapter 25 - Magnetic Effect of Current>Exercise - 1>Q 61

A $50$ -turn circular coil of radius $2.0$ cm carrying a current of $5.0 A$ is rotated in a magnetic field of strength $0.20 T .$

(a) What is the maximum torque that acts on the coil?

(b) In a particular position of the coil, the torque acting on it is half of this maximum. What is the angle between the magnetic field and the plane of the coil?

Two long wires carrying current in the same direction attract each other but two parallel beams of electrons moving in the same direction repel each other. Explain

Important Questions on Magnetic Effect of Current

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