Homework Answers
Solenoids are spring-shaped coils of wire commonly used in electromagnets. If you run an electric current through a solenoid, a magnetic field will be generated. The magnetic field can exert a force on charged particles that is proportional to its strength. To calculate the force from a solenoid's magnetic field, you can use this equation:
Force = charge x velocity of the charge x magnetic field strength
As you can see from the equation, to calculate force we first need to know the magnetic field strength, which is dependent on the characteristics of the solenoid. We can substitute these parameters into the force equation get:
Force = charge x velocity of the charge x (magnetic constant x number of turns in solenoid x current)
The calculation looks complicated, but really it's just multiplying a bunch of measurable variables together.
Write the equation for the force that a solenoidal electromagnet will exert on a passing charge:
Force = Q x V x (magnetic constant x N x I)
Q = charge of passing point charge V = velocity of point chart magnetic constant = 4 x pi x 10^-7 (reference 3) N = number of turns in solenoid I = current running through solenoid
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12-11 Consider a very long solenoid of N/I turns per unit length and radius R, Such...
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,...
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...
2. A solengid has n turns per unit length. The radius of solenoid is R. A...
2. A solengid has n turns per unit length. The radius of solenoid is R. A circular loop of wire with 10 turns and radius r<R lies along the axis of the solenoid near the middle of its length. If the current ie he circular loop is I, find the magnetic flux through the solenoid. 3. Two tiny wire loops with areas ar and az are situated a distance r apart. Find their mutual inductance,
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
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...
A long solenoid of cylindrical shape, having n turns of wire per unit length, carries a...
A long solenoid of cylindrical shape, having n turns of wire per unit length, carries a current I. Find the magnetic force acting on a small area, A, of the solenoid surface. Neglect magnetic permeability of the material inside the solenoid
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...
Ampère's Law A long solenoid of radius a consists of n = N/L coils per unit...
Ampère's Law A long solenoid of radius a consists of n = N/L coils per unit length and carries current to the right. Calculate the magnetic field inside and outside the solenoid far from the ends. 4,
The main magnet in an MRI machine is a superconducting solenoid 2.0 m long and 33...
The main magnet in an MRI machine is a superconducting solenoid 2.0 m long and 33 cm in radius. During normal operation, the current through the windings is 81 A, and the resistance of the windings is zero. The inductance of the solenoid is 89 H. (a) Calculate the turns per meter of the solenoid. (b) Calculate the magnitude of the magnetic field generated by the MRI machine during normal operations. (c) Calculate the magnetic flux through a single turn...
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.
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,...
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...
2. A solengid has n turns per unit length. The radius of solenoid is R. A circular loop of wire with 10 turns and radius r<R lies along the axis of the solenoid near the middle of its length. If the current ie he circular loop is I, find the magnetic flux through the solenoid. 3. Two tiny wire loops with areas ar and az are situated a distance r apart. Find their mutual inductance,
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
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...
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...
Ampère's Law A long solenoid of radius a consists of n = N/L coils per unit length and carries current to the right. Calculate the magnetic field inside and outside the solenoid far from the ends. 4,
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.
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