Homework Answers
A solenoid having n turns per unit length.
Solenoid having radius R. A circle loop of wire with 10 turns and radius r is smaller than R lies along the axis of solenoid near middle of its length. If the current in circular loop is 1. Find the magnetic flux through the solenoid.
For calculation of magnetic flux through closed surface.
Since number of incoming lines of outgoing lines so, and also,
Inductance
R is distance between coils
Let I1 be the current in 1st wire loop due to this magnetic flux is
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2. A solengid has n turns per unit length. The radius of solenoid is R. A...
solenoid current 4. A long solenoid with n turns per unit length and radius a is...
solenoid current
4. A long solenoid with n turns per unit length and radius a is surrounded by a single loop of wire of radius r, and resistance R. (The loop and solenoid are concentric, and r>a). The current in the solenoid varies aslo e-at. Find an expression for the current induced in the loop.
Example 7.10. A short solenoid (length l and radius a, with n turns per unit length)...
Example 7.10. A short solenoid (length l and radius a, with n turns per unit length) lies on the axis of a very long solenoid (radius b, n2 turns per unit length) as shown in Fig. 7.32. Curren I flows in the short solenoid. What is the flux through the long solenoid? FIGURE 7.32
Question 3 A long solenoid with n turns per unit length of current I is wrapped around a cylindri...
Question 3 A long solenoid with n turns per unit length of current I is wrapped around a cylindrical magnetic core of permeability μ μ0Hm The cylindrical core, extending along the z-axis, has radius α n turns per unit length, current I per turn Magnetic material of μ (a) If the solenoid is considered as infinite in length, it can be shown that the magnetic field, expressed in cylindrical coordinates, is: r> a Apply Ampere's law, using the rectangular path...
3. Find the magnitude of the induced electric field outside a long solenoid at a distance rZR from its central axis if the solenoid is of radius R and hasn turns of wire per unit length and carri...
3. Find the magnitude of the induced electric field outside a long solenoid at a distance rZR from its central axis if the solenoid is of radius R and hasn turns of wire per unit length and carries a time-varying current that varies sinusoidally as l = 1-cos cot where I-is maximum current and ω is the angular frequency of the current source. 4. A rectangular coil of N windings had an emf of 40 mV induced in it wher...
1. An infinite solenoid has n turns per unit length, a radius R, and carries a...
1. An infinite solenoid has n turns per unit length, a radius R, and carries a current I. The magnitude of the magnetic field inside the solenoid is given by B = Mon, pints along the solenoid, and vanishes outside. (a) Find the magnitude of the vector potential, A, at a radius r inside the solenoid. (b) Find the magnitude of the vector potential, A, at a radius r outside the solenoid. Check that your answers agree on the boundary,...
(13 pts total) A long solenoid of radius a, carrying n turns per unit length, is...
(13 pts total) A long solenoid of radius a, carrying n turns per unit length, is looped by a wire with resistance R, as shown in the figure below. a. (7 pts) If the current in the loop is increasing at a constant rate (dl/dt-k), what current 1. flows in the loop, and which way (left or right) does it pass through the resistor? (6 pts) If the current I in the solenoid is constant, but the solenoid is pulled...
A right circular solenoid of finite length L and radius a has N turns per unit...
A right circular solenoid of finite length L and radius a has N
turns per unit length and carries a current I. Show that the
magnetic induction on the cylinder axis in the limit NL→∞
Bz= μ₀NI(cosθ₁+cosθ₂)/2 where the angles are defined in the
figure.
A right-circular solenoid of finite length L and radius a has N turns per unit length and carries a current I. Show that the magnetic induction on the cylinder axis in the limit NL-oo is...
12-11 Consider a very long solenoid of N/I turns per unit length and radius R, Such...
12-11 Consider a very long solenoid of N/I turns per unit length and radius R, Such that the field inside is approximately uniform and the field outside is zero. Find the radial force on one turn of the winding, per unit length of circumference, from the magnetic energy. (a) Assume that the current I is maintained constant by a batterv (b) Repeat assuming that the flux remains constant and the system is isolated (with superconducting windings).
An infinite solenoid has radius b and n turns per unit length. The current varies in...
An infinite solenoid has radius b and n turns per unit length.
The current varies in time according to
(with positive defined as shown). A ring with radius
and resistance R is centred on the solenoid axis, with its plane
perpendicular to the axis. (a) What is the induced current in the
ring? (b) A given little piece of the ring will feel a magnetic
force. For what values of t is this force maximum? (c) What is the
effect...
Question 2: A circular solenoid of radius 2.5 cm has 400 turns and a length of...
Question 2: A circular solenoid of radius 2.5 cm has 400 turns and a length of 20 cm. The current in the solenoid changes at the rate of +38 A/s. a) Find the self-inductance L of the solenoid. b) Calculate the magnitude of the induced emf in the solenoid
solenoid current
4. A long solenoid with n turns per unit length and radius a is surrounded by a single loop of wire of radius r, and resistance R. (The loop and solenoid are concentric, and r>a). The current in the solenoid varies aslo e-at. Find an expression for the current induced in the loop.
Example 7.10. A short solenoid (length l and radius a, with n turns per unit length) lies on the axis of a very long solenoid (radius b, n2 turns per unit length) as shown in Fig. 7.32. Curren I flows in the short solenoid. What is the flux through the long solenoid? FIGURE 7.32
Question 3 A long solenoid with n turns per unit length of current I is wrapped around a cylindrical magnetic core of permeability μ μ0Hm The cylindrical core, extending along the z-axis, has radius α n turns per unit length, current I per turn Magnetic material of μ (a) If the solenoid is considered as infinite in length, it can be shown that the magnetic field, expressed in cylindrical coordinates, is: r> a Apply Ampere's law, using the rectangular path...
3. Find the magnitude of the induced electric field outside a long solenoid at a distance rZR from its central axis if the solenoid is of radius R and hasn turns of wire per unit length and carries a time-varying current that varies sinusoidally as l = 1-cos cot where I-is maximum current and ω is the angular frequency of the current source. 4. A rectangular coil of N windings had an emf of 40 mV induced in it wher...
1. An infinite solenoid has n turns per unit length, a radius R, and carries a current I. The magnitude of the magnetic field inside the solenoid is given by B = Mon, pints along the solenoid, and vanishes outside. (a) Find the magnitude of the vector potential, A, at a radius r inside the solenoid. (b) Find the magnitude of the vector potential, A, at a radius r outside the solenoid. Check that your answers agree on the boundary,...
(13 pts total) A long solenoid of radius a, carrying n turns per unit length, is looped by a wire with resistance R, as shown in the figure below. a. (7 pts) If the current in the loop is increasing at a constant rate (dl/dt-k), what current 1. flows in the loop, and which way (left or right) does it pass through the resistor? (6 pts) If the current I in the solenoid is constant, but the solenoid is pulled...
A right circular solenoid of finite length L and radius a has N
turns per unit length and carries a current I. Show that the
magnetic induction on the cylinder axis in the limit NL→∞
Bz= μ₀NI(cosθ₁+cosθ₂)/2 where the angles are defined in the
figure.
A right-circular solenoid of finite length L and radius a has N turns per unit length and carries a current I. Show that the magnetic induction on the cylinder axis in the limit NL-oo is...
12-11 Consider a very long solenoid of N/I turns per unit length and radius R, Such that the field inside is approximately uniform and the field outside is zero. Find the radial force on one turn of the winding, per unit length of circumference, from the magnetic energy. (a) Assume that the current I is maintained constant by a batterv (b) Repeat assuming that the flux remains constant and the system is isolated (with superconducting windings).
An infinite solenoid has radius b and n turns per unit length.
The current varies in time according to
(with positive defined as shown). A ring with radius
and resistance R is centred on the solenoid axis, with its plane
perpendicular to the axis. (a) What is the induced current in the
ring? (b) A given little piece of the ring will feel a magnetic
force. For what values of t is this force maximum? (c) What is the
effect...
Question 2: A circular solenoid of radius 2.5 cm has 400 turns and a length of 20 cm. The current in the solenoid changes at the rate of +38 A/s. a) Find the self-inductance L of the solenoid. b) Calculate the magnitude of the induced emf in the solenoid
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