A closely wound solenoid of 2000 turns and area of cross-section 1.6 x 10-4m2, carrying a current of 4.0 A, is suspended through its centre allowing it to turn in a horizontal plane.
(a) What is the magnetic moment associated with the solenoid?
(b) What is the force and torque on the solenoid if a uniform horizontal magnetic field of 7.5 x 10-2T is set up at an angle of 30º with the axis of the solenoid?
Number of turns on the solenoid,n = 2000
Area of cross-section of the solenoid, A= 1.6 ×10-4 m2
Current in the solenoid, I= 4 A
(a)The magnetic moment along the axis of the solenoid is calculated as:
M= nAI
= 2000 ×1.6 ×10-4 × 4
= 1.28 Am2
(b)Magnetic field, B = 7.5 ×10-2T
Angle between the magnetic field and the axis of the solenoid, θ= 30°
Torque, T = MB sin θ
= 1.28 x 7.5 x 10-2 sin30°
= 4.8 x 10-2 Nm
Since the magnetic field is uniform, the force on the solenoid is zero. The torque on the solenoid is
What is the force between two small charged spheres having charges of 2 x 10-7 C and 3 x 10-7 C placed 30 cm apart in air?
An infinite line charge produces a field of 9 × 104 N/C at a distance of 2 cm. Calculate the linear charge density.
A polythene piece rubbed with wool is found to have a negative charge of 3 × 10−7 C.
(a) Estimate the number of electrons transferred (from which to which?)
(b) Is there a transfer of mass from wool to polythene?
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A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm from the centre of the sphere is 1.5 × 103 N/C and points radially inward, what is the net charge on the sphere?
A point charge of 2.0 μC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?
A system has two charges qA = 2.5 × 10−7 C and qB = −2.5 × 10−7 C located at points A: (0, 0, − 15 cm) and B: (0, 0, + 15 cm), respectively. What are the total charge and electric dipole moment of the system?
The number density of free electrons in a copper conductor estimated in Example 3.1 is 8.5 x 1028 m-3. How long does an electron take to drift from one end of a wire 3.0 m long to its other end? The area of cross-section of the wire is 2.0 x 10-6 m2 and it is carrying a current of 3.0 A.
Answer the following questions:
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(b) Is Ohm's law universally applicable for all conducting elements? If not, give examples of elements which do not obey Ohm's law.
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(d) A high tension (HT) supply of, say, 6 kV must have a very large internal resistance. Why?
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(a) What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane?
(b) What is the flux through the same square if the normal to its plane makes a 60° angle with the x-axis?
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(b) The hysteresis loop of a soft iron piece has a much smaller area than that of a carbon steel piece. If the material is to go through repeated cycles of magnetisation, which piece will dissipate greater heat energy?
(c) 'A system displaying a hysteresis loop such as a ferromagnet, is a device for storing memory?' Explain the meaning of this statement.
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(e) A certain region of space is to be shielded from magnetic fields.
Suggest a method.
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Calculate the
(a) momentum, and
(b) de Broglie wavelength of the electrons accelerated through a potential difference of 56 V.
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