Advertisements
Advertisements
प्रश्न
A magnetic field of 100 G (1 G = 10−4 T) is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about 10−3 m2. The maximum current-carrying capacity of a given coil of wire is 15 A and the number of turns per unit length that can be wound round a core is at most 1000 turns m−1. Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.
Advertisements
उत्तर
Magnetic field strength, B = 100 G = 100 × 10−4 T
Number of turns per unit length, n = 1000 turns m−1
Current flowing in the coil, I = 15 A
Permeability of free space, μ0 = 4π × 10−7 T mA−1
Magnetic field is given by the relation,
`"B" = mu_0"nI"`
∴ `"nI" = "B"/mu_0`
= `(100 xx 10^-4)/(4pi xx 10^-7)`
= 7957.74
`≈ 8000 "A"/"m"`
If the length of the coil is taken as 50 cm, radius 4 cm, number of turns 400, and current 10 A, then these values are not unique for the given purpose. There is always a possibility of some adjustments with limits.
APPEARS IN
संबंधित प्रश्न
Obtain an expression for the energy stored in a solenoid of self-inductance ‘L’ when the current through it grows from zero to ‘I’.
A wire AB is carrying a steady current of 10 A and is lying on the table. Another wire CD carrying 6 A is held directly above AB at a height of 2 mm. Find the mass per unit length of the wire CD so that it remains suspended at its position when left free. Give the direction of the current flowing in CD with respect to that in AB. [Take the value of g = 10 ms−2]
In what respect is a toroid different from a solenoid?
A long solenoid of radius 2 cm has 100 turns/cm and carries a current of 5 A. A coil of radius 1 cm having 100 turns and a total resistance of 20 Ω is placed inside the solenoid coaxially. The coil is connected to a galvanometer. If the current in the solenoid is reversed in direction, find the charge flown through the galvanometer.
A circular coil of one turn of radius 5.0 cm is rotated about a diameter with a constant angular speed of 80 revolutions per minute. A uniform magnetic field B = 0.010 T exists in a direction perpendicular to the axis of rotation. Suppose the ends of the coil are connected to a resistance of 100 Ω. Neglecting the resistance of the coil, find the heat produced in the circuit in one minute.
A long solenoid is fabricated by closely winding a wire of radius 0.5 mm over a cylindrical nonmagnetic frame so that the successive turns nearly touch each other. What would be the magnetic field B at the centre of the solenoid if it carries a current of 5 A?
A copper wire having resistance 0.01 ohm in each metre is used to wind a 400-turn solenoid of radius 1.0 cm and length 20 cm. Find the emf of a battery which when connected across the solenoid will cause a magnetic field of 1.0 × 10−2 T near the centre of the solenoid.
A tightly-wound solenoid of radius a and length l has n turns per unit length. It carries an electric current i. Consider a length dx of the solenoid at a distance x from one end. This contains n dx turns and may be approximated as a circular current i n dx. (a) Write the magnetic field at the centre of the solenoid due to this circular current. Integrate this expression under proper limits to find the magnetic field at the centre of the solenoid. (b) verify that if l >> a, the field tends to B = µ0ni and if a >> l, the field tends to `B =(mu_0nil)/(2a)` . Interpret these results.
The length of a solenoid is 0.4 m and the number turns in it is 500. A current of 3 amp, is flowing in it. In a small coil of radius 0.01 m and number of turns 10, a current of 0.4 amp. is flowing. The torque necessary to keep the axis of this coil perpendicular to the axis of solenoid will be ______.
A solenoid is defined as a long helical coil of insulated wire with many closely spaced turns. Which geometric condition must it satisfy to be classified as a 'long' solenoid?
In the formula \(B = \mu_0 n I\) for the magnetic field inside a long solenoid, what does the quantity \(n\) represent?
A solenoid has a total of \(N\) turns wound uniformly over a length \(l\). What is the expression for the number of turns per unit length?
The net effect of a current-carrying solenoid is that it behaves like a bar magnet whose polarity is determined by which rule?
In the Ampere's Law derivation for a solenoid, if the Amperian loop has length \(l\) and the turns per unit length is \(n\), what is the total enclosed current \(I_{\text{enc}}\) when current \(I\) flows through the wire?
Applying Ampere's Law to the rectangular loop around a solenoid, the line integral equals \(Bl\) and the enclosed current is \(nlI\). Which sequence of steps correctly yields the magnetic field inside?
Solenoid valves used in washing machines and car engines serve what function?
A solenoid has length \(l = 0.5\) m, radius \(r = 1\) cm \(= 0.01\) m, total turns \(N = 500\), and carries current \(I = 5\) A. What is the turns per unit length?
