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प्रश्न
A circular coil of N turns and radius R carries a current I. It is unwound and rewound to make another coil of radius R/2, current I remaining the same. Calculate the ratio of the magnetic moments of the new coil and original coil.
उत्तर
The magnetic moment m of a current loop is the vector whose magnitude is equal to the area of the loop times the magnitude of the current flowing in it i.e.
m =N IA
Where, N = number of turns
Let m1 and m2 be the magnetic moments of circular original coil of radius ‘R’ and new coil of radius ‘R/2’.
Length of wire remains same. Thus,
`N (2piR) = N'(2pi(R/2))`
N' = 2N
Now,
`m_1NIA_1 =NI (pir_1^2) =NIpiR^2`
`m_2 = N'IA_2 = 2NI(pir_2^2) = 2NI(pi(R/2)^2) = 1/2NIpiR^2`
`m_2/m_1 = (1/2)/1 =1/2`
संबंधित प्रश्न
Seema’s uncle was advised by his doctor to have an MRI (Magnetic Resonance Imaging) scan of his brain. Her uncle felt it to be expensive and wanted to postpone it. When Seema learnt about this, she took the help of her family and also approached the doctor, who also offered a substantial discount. She then convinced her uncle to undergo the test to enable the doctor to know the condition of his brain. The information thus obtained greatly helped the doctor to treat him properly.
Based on the above paragraph, answer the following questions:
(a) What according to you are the values displayed by Seema, her family and the doctor?
(b) What could be the possible reason for MRI test to be so expensive?
(c) Assuming that MRI test was performed using a magnetic field of 0.1 T, find the minimum and maximum values of the force that the magnetic field could exert on a proton (charge = 1.6 x 10-19 C) moving with a speed of 104 m/s.
A circular coil carrying a current I has radius R and number of turns N. If all the three, i.e. the current
I, radius R and number of turns N are doubled, then, the magnetic field at its centre becomes:
(a) Double
(b) Half
(c) Four times
(d) One fourth
A charged particle is released from rest in a region of steady and uniform electric and magnetic fields which are parallel to each other. The particle will move in a ____________.
If a particle of charge 1012 coulomb moving along the `hat"x" -` direction with a velocity 102 m/s experiences a force of 1 o-s newton in `hat"y" -` direction due to magnetic field, then the minimum magnetic field is ____________.
The magnetic moment is NOT associated with ____________.
- If v is parallel to B, then path of particle is spiral.
- If v is perpendicular to B, then path of particle is a circle.
- If v has a component along B, then path of particle is helical.
- If v is along B, then path of particle is a circle.
The correct plot of the magnitude of magnetic field `vec"B"` vs distance r from centre of the wire is, if the radius of wire is R.
In the product `vec"F" = "q" (vec"υ" xx vec"B")`
= `"q" vec"υ" xx ("B"hat"i" +"B"hat"j" + "B"_0hat"k")`
For q = 1 and `vec"υ" = 2hat"i" + 4hat"j" + 6hat"k"` and
`vec"F" = 4hat"i" - 20hat"j" + 12hat"k"`
What will be the complete expression for `vec"B"`?
A charged particle would continue to move with a constant velocity in a region wherein ______.
- E = 0, B ≠ 0.
- E ≠ 0, B ≠ 0.
- E ≠ 0, B = 0.
- E = 0, B = 0.
A long straight wire carrying current of 25 A rests on a table as shown in figure. Another wire PQ of length 1 m, mass 2.5 g carries the same current but in the opposite direction. The wire PQ is free to slide up and down. To what height will PQ rise?
