Question

A current i is flowing through the loop. The direction of the current and the shape of the loop are as shown in the figure.The magnetic field at the centre of the loop is, $\frac{{\mu }_{0}i}{R}$ times

[ MA = R , MB = 2R, $\angle$DMA = 90°]

• A. $\frac{5}{16}$ , but out of the plane of the paper
• B. $\frac{5}{16}$, but into the plane of the paper
• C. $\frac{7}{16}$, but out of the plane of the paper
• D. $\frac{7}{16}$, but into the plane of the paper

Answer 1

The Correct Option is D

Explanation:
Given:
MA = R, MB = 2R, $\angle$ DMA = 90°We have to find the magnetic field at the center of the loop.The magnitude of magnetic field due to an arc of radius R and angle θ, carrying current at the center of the loop isB = π$\frac{{\mu }_{0}i}{4\mathrm{\pi R}}\theta$where, θ is the angle subtended by the arc.Given figure is redrawn below:

The magnetic field due to curve DA isBDA=πR(3π2)
Similarly, magnetic field due to the arc BC isBBC=π2R(π2)[ given MB=2R]
Also, the magnetic field due to the curve DC and AB isBDC=BAB=[since the angle between the current element and the position vector is zero, i.e. $\stackrel{\rightharpoonup }{dI}$ × $\stackrel{\rightharpoonup }{r}$ =0
Now, the resultant magnetic field at the centre M isBnet =BDA+BAb+BBC+BCD
⇒Bnet=πR(3π2)++8πR(π2)+
⇒Bnet=R[32+1]⇒Bnet=R×[6+1]⇒Bnet=716R
Using the right-hand thumb rule for the magnetic field, the direction of the magnetic field is into the plane of the paper, as the direction of the current is clockwise.
Hence, the correct option is (D).

Answer 2

Ans. Fleming’s Left-Hand Rule and Fleming’s Right-Hand Rule are important rules for magnetism and electromagnetism. Developed by John Ambrose Fleming in the late 19th century, Fleming’s rules are also used to find the direction of motion in an electric motor. A current-carrying conductor experiences a force perpendicular to the field and the current direction when found in an external magnetic field.

• Fleming’s left-hand rule states that if we arrange our thumb, index finger (or forefinger), and middle finger perpendicular to each other, then they denote the directions of Motion, Current, and Magnetic Field respectively. 
• Fleming’s right-hand rule is used to determine the direction of induced current. This rule is used to understand the functioning of electric motors by determining the direction of the force.

Fleming’s Left Hand and Right-Hand rules do not determine the magnitude; instead, they only show the direction of – the magnetic field, current, and force – when the direction of the other two parameters is already known

• Electric charges in motion produce a magnetic field.
• The region around a magnet, where magnetism is sensed, is known as the magnetic field.
• It is a force field that applies a force on objects around, even iron when they come into contact with it.
• Magnetic fields may even spread in a vacuum since they do not need a medium to do so.
• The magnetic field differs from the electric field in that it has a greater ability to store energy, which enables it to be employed in all electromechanical devices, including transformers, motors, and generators. 
• A magnetic field is a vector field where magnetic forces may be felt, usually near a magnet, an electric current, or a shifting electric field.
• Moving electric charges and basic particles' intrinsic magnetic moments, which are connected with a fundamental quantum feature known as "spin," may produce magnetic fields.
• The phrases magnetic field and electric field are often connected and serve as the primary building blocks of electromagnetic force.