GAT Test - 7

CONCEPT:

EXPLANATION:

• A charge in a static field produces an electric field only, a charge in motion produces both electric and magnetic fields. 
• When the charge is accelerated the electric and magnetic fields produced are time-varying. 
• Therefore, all-electric charges, whether static or in motion with respect to an observer gives rise to the electric field. Hence option 1 is correct.
• If a charged particle is not moving i.e., in static conditions then it will not produce the magnetic field. Therefore option 2 is not true.

Concept:

Solenoid:

• The solenoid is a type of electromagnet, the purpose of which is to generate a controlled magnetic field through a coil wound into a tightly packed helix.
• The magnetic field is formed around the coil when an electric current passes through it and draws the plunger in.

• The magnetic field at the center of the solenoid, B = μ₀ nI, where, n = number of turns per unit length, I = current 

Explanation:

• The magnetic field inside a long straight solenoid-carrying current is the same at all points.
• It is because the magnetic field in the solenoid is constant because the lines are completely parallel to each other.

CONCEPT:

• Right-hand thumb rule: According to this rule, if we imagine the linear wire conductor to be held in the grip of the right hand so that the thumb points in the direction of the current, then the curvature of the fingers around the conductor will represent the direction of the magnetic field lines.

EXPLANATION:

• From the above, it is clear that according to the Right-hand thumb rule, the thumb points in the direction of the electric current in a straight current-carrying wire.

Additional Information

• Fleming Left-hand rule gives the force experienced by a charged particle moving in a magnetic field or a current-carrying wire placed in a magnetic field.
  • It states that stretch the thumb, the forefinger, and the central finger of the left hand so that they are mutually perpendicular to each other.
  • If the forefinger points in the direction of the magnetic field, the central finger points in the direction of motion of charge, then the thumb points in the direction of force experienced by positively charged particles.

Concept:

• Magnetic fields exert forces on moving charges, and so they exert forces on other magnets,
• The magnitude of the magnetic force on a moving charge is given by 

• Where, q is the magnitude of the electric charge, in C, V is the magnitude of the velocity of the charge, in m/s, B is the magnitude of the external magnetic field (T) in which the charge is moving, θ is the angle between v and B.

The direction of the magnetic force on a moving charge is determined by using the Right-Hand-Rule

• Place your right hand in the direction of v.  Next, close your hand in the direction of B.
• Your thumb points in the direction of the force on a positive charge.
• The direction of the force on a negative charge is opposite to the direction of the force on a positive charge.

Explanation:

• The direction of the magnetic force on a moving charge is determined by using the Right-Hand-Rule, 
• When we place our right hand in the direction of v.  and close our hand in the direction of B.
• Our thumb points in the direction vertically upward.
• But the direction of the force on a negative charge is opposite to the direction of the force on a positive charge. and electron is a negative charge, so the direction of the magnetic force is vertically downward.

OR

From the palm rule, we can also calculate the force direction. If we point out the thumb direction in the direction of electron movement and the fingers in the direction of field direction, then the direction of palm gives the direction of force on the electron.

Explanation: 

We know when a moving charge particle enters a magnetic field in a direction at right angles to the lines of force then the magnetic field changes the direction of charge.

This leads to the circular motion of moving charge particles within the magnetic field.

here, Centripetal force = Lorentz force

where, v is the velocity of the charged particles, B is the magnetic field, m is the mass of

the particle and r is the radius of the circular path and  θ is the angle between the

magnetic field and velocity. 

Solving for radius we get,

Since momentum p and Magnetic field B are the same and charges on proton and electron both are the same then the radius will also be the same for both. hence, the assertion is true. 

The mass of the proton is 1800 times the mass of the electron and hence reason is also true. 

But the radius of the path does not depend on the mass and hence reason is not the correct explanation of the assertion

Hence, the correct option is (2)

CONCEPT:

Magnetic Field Lines:

• The magnetic field lines are invisible lines of magnetic force that never cross each other.
• And can be drawn putting iron dust or compass in the magnetic field of the bar magnet.
• Magnetic field lines are continuous and always form a unique closed loop around the magnet.
• Magnetic field lines have a definite direction from North to South.
• Magnetic field lines of force that are close together indicate a strong magnetic field.
• Magnetic field lines of force that are farther apart indicate a weak magnetic field.

EXPLANATION:

• Magnetic field lines never intersect with each other.

Important Point

• Unlike poles means North and South attract each other.
• Like poles means North and North repels each other.

CONCEPT:

The magnetic field at point O due to a straight conductor is given by:

where B is the magnetic field at the center, μ0 permeability of the medium I is the current in the circular loop, and d is the distance from the wire to that point.

EXPLANATION:

The magnitude of the magnetic field B at a distance r from an infinitely long straight conductor through which a current I is flowing is given by:

Hence the correct answer is option 1.

Concept:

Current Carrying Coil: 

• When an electric current is passed through a closed circular current carrying wire then the magnetic field is observed in the surrounding which is strong at the center as compared to outside.
• The current carrying coil is just like a magnet.

Magnetic Field: 

• The field around a moving charge or magnetic material up to which magnetic effect or force due to magnetism can be experienced is called a magnetic field.
• The magnetic field at the center the of circular current carrying coil is given by the mathematical expression:

• where I is current through the circular loop, N is the total no of turns in the circular current carrying loop and , r is the radius of the circular current carrying loop and μ0 is the permeability of free space

Explanation:

Let us consider a circular loop of wire of radius r carrying current I.

We have to calculate the magnetic field at the center of the loop. 

First of all the entire loop is divided into a large o of small current elements.

We have considered one such small current element  of the loop.

According to Biot-Savart law, the magnetic field at the center due to this element is

The magnetic field  at the center of the current carrying loop

• proportional to current (I)
• inversely proportional to radius (r)
• proportional to the number of turns (N)

Important Points

Biot-Savart Law:

• T he law that gives the magnetic field generated by a constant electric current is Biot-savart law.
• Let us take a current carrying wire of current I and we need to find the magnetic field at a distance r from the wire then it is given by:

Where,

μ₀ = the permeability of free space/vacuum (4π × 10^-7 T.m/A),

dl = small element of wire

 the unit position vector of the point where we need to find the magnetic field.

CONCEPT:

• Fleming Left-hand rule gives the force experienced by a charged particle moving in a magnetic field or a current-carrying wire placed in a magnetic field.
• It states that "stretch the thumb, the forefinger, and the central finger of the left hand so that they are mutually perpendicular to each other.
• If the forefinger points in the direction of the magnetic field, the central finger points in the direction of motion of charge, then the thumb points in the direction of force experienced by positively charged particles."

EXPLANATION:

• According to question

1. Forefinger (Index finger): Represents the direction of the magnetic field (magnetic flux). 
2. Middle finger: Represents the direction of motion of charge (current). Therefore option 2 is correct.
3. The thumb is pointing out of the paper: Represents the direction of force experienced by positively charged particles.

Concept:

Torque:

• ​ It is defined as the product of the magnitude of the force and the perpendicular distance of the line of action of a force from the axis of rotation.
• Formula, τ = rFsinθ , where r = perpendicular distance, F = force, θ = angle between force and perpendicular distance
• The SI unit of torque is N-m.

Torque in a current loop:

• ​Let us consider a rectangular loop such that it carries a current of magnitude I.

• If we place this loop in a magnetic field, it experiences a torque but no net force, quite similar to what an electric dipole experiences in a uniform electric field.
• The torque acting on the coil is calculated as, τ = NIAB sinθ where N = number of turns, I = current, A = area of the loop, B = magnetic field, θ = angle between area and magnetic field. 

Calculation:

Given,

The number of turns, N = 100 turns

The current in the coil, I = 80 mA

Angle, θ = 30º

The radius of the circular coil, r = 0.50 m

The magnitude of the magnetic field, B = 4.0 T

The torque acting on the coil is calculated as, τ = NIAB sinθ 

τ = 100 × 80 × 10^-3 × π × (0.50)² × 4.0 × sin 30º

τ = 4π N m

Hence, the magnitude of torque acting on the coil is 4π N m.