Two identical wires A and B, each of length ‘l’, carry the same current I. Wire A is bent into a circle of radius R and wire B is bent to form a square of side ‘a’. If BA and BB are the values of the magnetic field at the centres of the circle and square respectively, then the ratio BA /BB is:
C.
Magnetic field in case of circle of radius R, we have
Magnetic field in case of square of side we get
Hysteresis loops for two magnetic materials A and B are given below:
These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use:
A for electric generators and transformers.
A for electromagnets and B for electric generators
A for transformers and B for electric generators.
A for transformers and B for electric generators.
D.
A for transformers and B for electric generators.
Area of the hysteresis loop is proportional to the net energy absorbed per unit volume by the material, as it is taken over a complete cycle of magnetisation.
For electromagnets and transformers, energy loss should be low.
i.e thin hysteresis curves.
Also |B|→0 When H = 0 and |H| should be small when B →0.
An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to:
80 H
0.08 H
0.044 H
0.044 H
D.
0.044 H
I = 10 A, V = 80 V
R = V/I = 80/10 = 8Ω and ω = 50 Hz
For AC circuit, we have 
A galvanometer having a coil resistance of 100 Ω gives a full-scale deflection, when a current of 1 mA is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full-scale deflection for a current of 10 A, is:
0.01 Ω
2 Ω
0.1 Ω
0.1 Ω
A.
0.01 Ω
Maximum voltage that can be applied across the galvanometer coil = 100 Ω x 10-3 A = 0.1
If Rs is the shunt resistance, then
Rs x 10 A = 0.1 V
Rs = 0.01 Ω
(a) Using Biot-Savart’s law, derive the expression for the magnetic field in the vector form at a point on the axis of a circular current loop.
(b) What does a toroid consist of? Find out the expression for the magnetic field inside a toroid for N turns of the coil having the average radius r and carrying a current I. Show that the magnetic field in the open space inside and exterior to the toroid is zero.
Biot-Savart law states that the magnetic field strength (dB) produced due to a current element of current I and length dl at a point having position vector to current element is given by,
where, μ0 is permeability of free space.
The magnitude of magnetic field is given by,
; θ is the angle between the current element and position vector.
Magnetic field at the axis of a circular loop :
Consider a circular loop of radius R carrying current I. Let, P be a point on the axis of the circular loop at a distance x from its centre O. Let, be a small current element at point A.
Magnitude of magnetic induction dB at point P due to this current element is given by,
... (1)
The direction of 
is perpendicular to the plane containing 
.
Angle between 
Therefore, 
... (2)
The magnetic induction 
can also be resolved into two components, PM and PN’ along the axis and perpendicular to the axis respectively. Thus if we consider the magnetic induction produced by the whole of the circular coil, then by symmetry the components of magnetic induction perpendicular to the axis will be cancelled out, while those parallel to the axis will be added up.
Thus, resultant magnetic induction 
at axial point P is given by,
Therefore the magnitude of resultant magnetic induction at axial point P due to the whole circular coil is given by,
B = 
Therefore, 
b) A long solenoid on bending in the form of closed ring is called a toroidal solenoid.
i) For points inside the core of a toroid,
As per Ampere’s circuital law, 
where, I is the current in the solenoid.
So, resultant net current = NI
Since no current is flowing through the points in the open space inside the toroid.
Therefore, I = 0.
So, 
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