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Physics

Magnetism And Maxwell S Equations

18 previous year questions.

Volume: 18 Ques

Yield: Medium

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Chapter Questions
18 MCQs

PYQ 2017

medium

physics ID: iit-jam-

Consider a thin long insulator coated conducting wire carrying current . It is now wound once around an insulating thin disc of radius to bring the wire back on the same side, as shown in the figure. The magnetic field at the center of the disc is equal to:

PYQ 2017

medium

physics ID: iit-jam-

Consider a circular parallel plate capacitor of radius with separation between the plates (). The plates are placed symmetrically about the origin. If a sinusoidal voltage is applied between the plates, which of the following statement(s) is (are) true?

The maximum value of the Poynting vector at is .

The average energy per cycle flowing out of the capacitor is .

The magnetic field inside the capacitor is constant.

The magnetic field lines inside the capacitor are circular with the current flowing in the -direction.

PYQ 2018

medium

physics ID: iit-jam-

An infinitely long solenoid, with its axis along, carries a current . In addition, there is a uniform line charge density along the axis. If is the energy flux, in cylindrical coordinates, then

is along

is along

has non zero components along and

is along

04

PYQ 2018

medium

physics ID: iit-jam-

$A long solenoid is carrying a time dependent current such that the magnetic field inside has the form, where is along the axis of the solenoid. The displacement current at the point on a circle of radius in a plane perpendicular to the axis$

1

$is inversely proportional to and radially outward.$

2

$is inversely proportional to and tangential.$

3

$increases linearly with time and is tangential.$

4

$is inversely proportional to and tangential.$

Official Solution

Correct Option: $(2)$

$Step 1: Use Maxwell-Ampère law with displacement current. . Given, the time derivative is . Step 2: Apply Faraday's law to circulating electric field. The changing magnetic field induces a circulating (tangential) electric field around the axis: . Since, . Step 3: Find E-field direction and magnitude. For circular symmetry: . Thus . Therefore, the displacement current density (linear in time). Step 4: Direction of the field. Induced electric field circulates around the solenoid \Rightarrow tangential direction. Step 5: Conclusion. The displacement current increases linearly with time and is tangential.$

05

PYQ 2018

medium

physics ID: iit-jam-

$Consider an electromagnetic plane wave, where is the wavelength and is the speed of light. The value of is ............. (Specify answer up to two digits after the decimal point.)$

Official Solution

Correct Option: $(1)$

$Step 1: Understand E-field polarization. The electric field direction is given by the vector . The wave propagates in direction . Step 2: Use orthogonality of and .} . Step 3: Solve for . \Rightarrow . Step 4: Convert to magnitude of full polarization vector. Total magnitude = .$

06

PYQ 2018

medium

physics ID: iit-jam-

$A current flows through the sides of an equilateral triangle of side . The magnetic field at the centroid is$

1

2

3

4

Official Solution

Correct Option: $(1)$

$Step 1: Use magnetic field from a finite wire. For each side of the triangle: . Step 2: Geometry of equilateral triangle. Distance from centroid to each side = . Angles are each: . Step 3: Field of one side. . Step 4: Total field (three sides). . Conclusion. The magnetic field at the centroid is .$

07

PYQ 2019

medium

physics ID: iit-jam-

$Which one of the following is an impossible magnetic field ?$

1

2

3

4

Official Solution

Correct Option: $(4)$

$Step 1: Understanding the conditions for a magnetic field. A magnetic field must satisfy the condition (Gauss's law for magnetism), meaning that the divergence of the magnetic field must be zero. We will check the divergence for each option. Step 2: Calculating the divergence for each option. - Option (A): . The divergence is zero, so this is a valid magnetic field. - Option (B): . The divergence is zero, so this is a valid magnetic field. - Option (C): . This does not give zero, so this is an impossible magnetic field. - Option (D):, which gives zero for specific values, so it can be a valid magnetic field. Step 3: Conclusion. The correct answer is (C) because the divergence does not satisfy the condition .$

08

PYQ 2020

medium

physics ID: iit-jam-

$The magnetic fields in tesla in the two regions separated by the plane are given by and . The magnitude of the surface current density at the interface between the two regions is . Given the permeability of free space, the value of is ............... . (Round off to 2 decimal places)$

Official Solution

Correct Option: $(1)$

$Step 1: Identify componentsAt :Normal direction: Tangential directions: and Region 1:Normal: TTangential: TRegion 2:Normal: TTangential: TStep 2: Calculate surface current densityThe discontinuity in tangential gives surface current: $ \hat{n} = \hat{z} \vec{H} = \frac{\vec{B}}{\mu_0} \hat{z} \times \hat{x} = \hat{y} \hat{z} \times \hat{y} = -\hat{x} \alpha = 2.87$Answer: 2.87$

09

PYQ 2020

medium

physics ID: iit-jam-

$For electric and magnetic fields, and, due to a charge density and a current density, which of the following relations is/are always correct?$

1

2

3

4

Official Solution

Correct Option: $(2)$

$Analyzing Maxwell's equations and electromagnetic relations:(A) From Faraday's law: $ \vec{B} \vec{\nabla} \times \vec{E} \neq 0 \vec{\nabla} \cdot \vec{B} = 0 \vec{\nabla} \cdot \vec{J} - \frac{\partial \rho}{\partial t} = 0 \vec{\nabla} \cdot \vec{J} = -\frac{\partial \rho}{\partial t} \vec{\nabla} \cdot \vec{J} - \frac{\partial \rho}{\partial t} = -\frac{\partial \rho}{\partial t} - \frac{\partial \rho}{\partial t} = -2\frac{\partial \rho}{\partial t} \neq 0 \vec{\nabla} \cdot \vec{J} + \frac{\partial \rho}{\partial t} = 0 \vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$This is the Lorentz force law, which gives the force on a charged particle moving in electromagnetic fields. This is a fundamental law and is always true.ALWAYS correct Answer: (B) and (D) are always correct$

10

PYQ 2020

medium

physics ID: iit-jam-

$Consider an annular region in free space containing a uniform magnetic field in the -direction, schematically represented by the shaded region in the figure. A particle having charge and mass starts from point in the -direction with constant speed . If the radii of inner and outer circles are and, respectively, the minimum magnetic field required so that the particle returns to the inner circle is:$

1

2

3

4

Official Solution

Correct Option: $(2)$

$Step 1: Concept of circular motion in a magnetic field. The radius of circular motion of a charged particle moving in a magnetic field is Step 2: Condition for returning to the inner circle. The particle must just touch the outer boundary before returning to the starting point, forming a semicircular trajectory between and . At the maximum deflection, the center of circular motion lies along the -axis. The geometry gives: Step 3: Substitute radius. Step 4: Conclusion. The minimum magnetic field required is .$

11

PYQ 2022

hard

physics ID: iit-jam-

$A circular loop of wire with radius R is centered at the origin of the xy-plane. The magnetic field at a point within the loop is,, where k is a positive constant of appropriate dimensions. Neglecting the effects of any current induced in the loop, the magnitude of the induced emf in the loop at time t is$

1

2

3

4

Official Solution

Correct Option: $(1)$

$To find the magnitude of the induced emf in the loop, we need to use Faraday's law of electromagnetic induction, which states that the induced emf in a closed loop is equal to the negative rate of change of magnetic flux through the loop: Here, is the magnetic flux through the loop, which is given by: Since the magnetic field is given as and the area element is for a circular loop in polar coordinates, the magnetic flux becomes: This simplifies to: First, we integrate with respect to from to : Now, integrate with respect to from to : Thus, the magnetic flux becomes: The induced emf is then the negative derivative of the magnetic flux with respect to time: Calculating the derivative: Hence, the induced emf is: The magnitude of the induced emf is: Thus, the correct answer is .$

12

PYQ 2022

hard

physics ID: iit-jam-

$Consider a conical region of height h and base radius R with its vertex at the origin. Let the outward normal to its base be along the positive z-axis, as shown in the figure. A uniform magnetic field, exists everywhere. Then the magnetic flux through the base () and that through the curved surface of the cone () are$

1

2

3

4

Official Solution

Correct Option: $(4)$

$The problem involves calculating the magnetic flux through the base and the curved surface of a cone placed in a uniform magnetic field, . Determine the magnetic flux through the base : The base of the cone is a circular plane with radius, and the area vector is along the positive z-axis. The magnetic field is uniform and also along the z-axis. The area of the base is . The magnetic flux through the base is given by: Determine the magnetic flux through the curved surface : The magnetic field is uniform and parallel to the z-axis. The curved surface of the cone has no component of area perpendicular to the z-axis. This is because any elemental area on the curved surface has its normal perpendicular to the z-axis. Therefore, the magnetic flux through the curved surface is: Using Gauss's Law for magnetism, we know that the net magnetic flux through a closed surface is zero. The flux through the base and the curved surface must sum to zero, verifying: . However, the base flux is outward (positive), so the net result through the closed surface including open base and curved cone remains balanced. Thus, the correct answer is:$

13

PYQ 2022

medium

physics ID: iit-jam-

$A uniform magnetic field, where exists as shown in the figure. A charged particle of mass m and charge is released at the origin, in the yz-plane, with a velocity directed at an angle = 45° with respect to the positive z-axis. Ignoring gravity, which one of the following is TRUE.$

1

$The initial acceleration$

2

$The initial acceleration$

3

$The particle moves in a circular path$

4

$The particle continues in a straight line with constant speed$

Official Solution

Correct Option: $(1)$

$To solve this problem, we need to analyze the motion of a charged particle in a magnetic field. Let's break down the given setup: The magnetic field is . The charge is positive, and the particle mass is . The particle is released with velocity at an angle with respect to the z-axis. The velocity can be resolved into components: Using the right-hand rule for a velocity component perpendicular to the magnetic field: The magnetic force is given by . In this setup, the z-component of velocity does not contribute to the force as it is parallel to the magnetic field. Only the y-component of velocity contributes: The acceleration of the particle is given by: This shows the acceleration is initially in the x-direction, matching option: The initial acceleration Conclusion: The correct answer is that the initial acceleration is .$

14

PYQ 2023

medium

physics ID: iit-jam-

$A small bar magnet is dropped through different hollow copper tubes with same length and inner diameter but with different outer diameter. The variation in the time (t) taken for the magnet to reach the bottom of the tube depends on its wall thickness (d) as$

1

2

3

4

Official Solution

Correct Option: $(3)$

$To solve this question, we need to understand the physics behind the problem. When a bar magnet is dropped through a conductive non-magnetic hollow tube, like a copper tube, it induces eddy currents in the walls of the tube. These eddy currents, in turn, produce a magnetic field that opposes the motion of the magnet due to Lenz's law, which states that the direction of induced current will be such that it will oppose the change that caused it. The amount of eddy current induced is directly related to the thickness of the tube walls, denoted by d . As the thickness increases, the resistance to the flow of eddy currents decreases, which means that more current is generated for the same rate of change of magnetic flux. In terms of the graph options provided, the time t that the magnet takes to reach the bottom of the tube is affected by these eddy currents. Greater wall thickness leads to greater eddy current production, which effectively increases the time due to increased opposing forces acting on the magnet. Thus, a thicker wall induces larger eddy currents and hence more magnetic damping, slowing the magnet down more significantly. Therefore, the relationship between time t and wall thickness d should show an increasing trend. The correct graph should depict this relationship as increasing. Thus, among the provided options, the correct answer is the graph that shows time t increasing with wall thickness d : This graph clearly demonstrates that as the wall thickness increases, so does the time taken by the magnet to reach the end of the tube, which is consistent with our analysis based on Lenz's law and eddy current phenomena.$

15

PYQ 2023

medium

physics ID: iit-jam-

$Suppose the divergence of magnetic field is nonzero and is given as, where 𝜇 0 is the permeability of vacuum and 𝜌 m is the magnetic charge density. If the corresponding magnetic current density is, then the curl of the electric field is$

1

2

3

4

Official Solution

Correct Option: $(4)$

$To solve this problem, we need to consider the modified Maxwell's equations that account for the possibility of magnetic monopoles. The divergence of the magnetic field in this case is given by: where is the permeability of vacuum and is the magnetic charge density. According to the modified Maxwell's equations, the curl of the electric field in the presence of a magnetic current density is given by: This equation indicates that the change in the magnetic field over time and the magnetic current density both contribute to the curl of the electric field. Now, let us match this derived expression with the provided options: - does not match because there's no negative sign with the current density. - not correct due to incorrect signs and factors. - This option also has an incorrect factor. - Correct match as it incorporates both the time derivative of the magnetic field and the magnetic current density with the correct factor and signs. Thus, the correct answer is:$

16

PYQ 2024

medium

physics ID: iit-jam-

$A time dependent magnetic field inside a long solenoid of radius 0.05m is given by (𝑡) = 𝐵 0 sin 𝜔𝑡 . If 𝜔=100rad/s and 𝐵 0 = 0.98Weber/m 2, then the amplitude of the induced electric field at a distance of 0.07m from the axis of the solenoid is ______V/m. (Rounded off to two decimal places)$

Official Solution

Correct Option: $(1)$

$Induced Electric Field in a Solenoid The induced electric field at a distance from the axis of a solenoid is obtained from Faraday’s law of electromagnetic induction : where is the magnetic flux through the solenoid. 1. Case 1: The magnetic flux through a circle of radius inside the solenoid is: 2. Case 2: The magnetic flux through the solenoid remains constant and is determined by its radius : Step 1: Expression for the Induced Electric Field For, the induced electric field is given by: Step 2: Substituting Substituting, the time derivative is: Thus, the induced electric field is: Step 3: Substituting Given Values Weber/m² rad/s Step 4: Simplifying the Expression Final Answer The amplitude of the induced electric field is 1.71 V/m .$

17

PYQ 2024

medium

physics ID: iit-jam-

$A 15.7mW laser beam has a diameter of 4mm. If the amplitude of the associated magnetic field is expressed as, the value of A is: (𝜀 0 is the free space permittivity and 𝑐 is the speed of light)$

1

$50$

2

$35.4$

3

$100$

4

$70.8$

Official Solution

Correct Option: $(1)$

$Step 1: Calculate the intensity of the laser beam The power of the laser beam is, and the diameter of the beam is . The area of the beam cross-section is: The intensity is given by: Substituting the values: Step 2: Relate intensity to the magnetic field amplitude The intensity of an electromagnetic wave is related to the amplitude of the magnetic field by: where: - is the permeability of free space, - is the speed of light. Step 3: Solve for Rearrange the formula to solve for : Using, the expression becomes: Therefore: Comparing with the given form, we identify: Step 4: Calculate Substituting : Final Answer: The value of is: 50 .$

18

PYQ 2024

medium

physics ID: iit-jam-

$The magnitudes of spin magnetic moments of electron, proton and neutron are μ e, μ p and μ n, respectively. Then$

1

$μ e >μ p >μ n$

2

$μ e =μ p >μ n$

3

$μ e <μ p <μ n$

4

$μ e <μ p <μ n$

Official Solution

Correct Option: $(1)$

$The spin magnetic moments of elementary particles such as the electron, proton, and neutron are determined by their intrinsic properties, such as charge and mass. Key Observations: The electron has a much larger spin magnetic moment than the proton or neutron due to its: Smaller mass Higher charge-to-mass ratio The proton and neutron have comparable masses, but: The neutron has no net charge, resulting in a much smaller magnetic moment. Order of Magnetic Moments: The correct order of magnetic moments is: Conclusion: Thus, the correct answer is: Option (A)$

About Magnetism And Maxwell S Equations - IIT-JAM-PH

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Magnetism And Maxwell S Equations

High-Yield Trend

Chapter Questions 18 MCQs

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Induced Electric Field in a Solenoid

1. Case 1:

2. Case 2:

Step 1: Expression for the Induced Electric Field

Step 2: Substituting

Step 3: Substituting Given Values

Step 4: Simplifying the Expression

Final Answer

Official Solution

Step 1: Calculate the intensity of the laser beam

Step 2: Relate intensity to the magnetic field amplitude

Step 3: Solve for

Step 4: Calculate

Final Answer:

Official Solution

Key Observations:

Order of Magnetic Moments:

Conclusion:

About Magnetism And Maxwell S Equations - IIT-JAM-PH

Frequently Asked Questions

Why focus on Magnetism And Maxwell S Equations PYQs?

How to best use this analysis?

Chapter Questions
18 MCQs

1. Case 1: $r%20%3C%20R$

2. Case 2: $r%20%3E%20R$

Step 2: Substituting $B(t)$

Step 3: Solve for $B_0$

Step 4: Calculate $A$