Magnetic Field Due to Straight Current Carrying Wire

Practice Questions:

Question 21: difficult

What will be the resultant magnetic field at origin due to four infinite length wires. If each wire produces magnetic field ‘B’ at origin:

1. 4B

2. √2 B

3. 2√2 B

4. Zero

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Question 22: difficult

A current I flows in a thin wire, shaped as regular polygon of n sides which can be
inscribed in a circle of radius R. The magnetic field induction at the centre of polygon due to
one side of the polygon is :

1. \[tan\frac{\pi}{n} tesla\]

2. \[\frac{\mu_{0}I}{\pi R}\left[ tan\frac{\pi}{n} \right] tesla\]

3. \[\frac{\mu_{0}I}{2\pi R}\left[ tan\frac{\pi}{n} \right] tesla\]

4. \[\frac{\mu_{0}I}{2\pi R}\left[ cos\frac{\pi}{n} \right]\]

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Question 23: moderate

Consider a set of six infinite long straight parallel wires arranged perpendicular to the plane of paper in a hexagon as shown. The length of the each side of the hexagon is 3 cm. What is the magnitude and direction of the magnetic field at point P ?

1. 20 μT

2. 40 μT

3. 60 μT

4. 80 μT

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Question 24: easy

Assertion (A): Two long parallel conductors carrying currents in the same direction experience a force of attraction.

Reason (R): The magnetic fields produced in the space between two long parallel current carrying conductors (by each of these conductors) are in the same direction.

1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (3) (A) is true but (R) is false

4. (4) Both (A) and (R) are false

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Parallel currents in the same direction attract, so (A) is true. For two parallel currents in the same direction, the magnetic fields in the space between them are in opposite directions (e.g., one into the page, one out of the page by Right Hand Rule). Therefore, (R) is false.

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Question 25: easy

Assertion (A): A system can not have magnetic moment when its net charge is zero.

Reason (R): Magnetic field arises due to charge in motion.

1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

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Assertion (A) is false. A current loop, for instance, has zero net charge but possesses a magnetic moment. Reason (R) is true; magnetic fields are indeed generated by moving charges (currents). Since Assertion (A) is false, options A, B, and C are incorrect. Option D states both (A) and (R) are false, which is partially incorrect as (R) is true. However, being the only option where (A) is stated as false, we choose it.

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Question 26: easy

Assertion (A): The magnetic field induction due to an infinite long current carrying solid cylindrical conductor of radius \(R\), at a distance \(R/2\) and \(2R\) from its axis is same.

Reason (R): An infinite long current carrying solid cylindrical conductor is a source of uniform magnetic field.

1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

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Assertion (A) is true: Using Ampere's Law, \(B(R/2) = \frac{\mu_0 I (R/2)}{2\pi R^2} = \frac{\mu_0 I}{4\pi R}\) and \(B(2R) = \frac{\mu_0 I}{2\pi (2R)} = \frac{\mu_0 I}{4\pi R}\).

Reason (R) is false: The magnetic field is not uniform; it varies linearly inside (\(B \propto r\)) and inversely outside (\(B \propto 1/r\)). Thus, A is true and R is false.

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Question 27: easy

Assertion (A): If a uniform current carrying loop is placed in uniform magnetic field perpendicular to plane of loop. Tension or compression is created in loop.

Reason (R): Net force on any closed loop in uniform magnetic field is zero.

1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

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Assertion (A) is true: Magnetic forces \(I d\vec{l} \times \vec{B}\) on segments act radially, causing tension or compression. Reason (R) is true: For a uniform \(\vec{B}\), \(\vec{F}_{net} = I \oint d\vec{l} \times \vec{B} = 0\). However, zero net translational force does not explain the internal tension/compression. Both are true, but (R) is not the explanation for (A).

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