Homework Answers
The magnetic dipole moment and
magnetic field due to circular disc are calculated above.
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1. A thin circular disk of radius R carries a uniform surface charge o and is...
4. A flat disk of radius R, carrying a uniform charge density + ơ, is rotating at a constant angu...
4. A flat disk of radius R, carrying a uniform charge density + ơ, is rotating at a constant angular velocity o. a) What is the magnitude of the surface current density K at a distance s from the ccnicr f the disk? b) Calculate the magntic field (magnitude and direction) at a point P located on the axis of the disk. [Hint: Treat the disk as a collection of rings of width dr. The current in each ring is...
Problem 5: A thin (non-conducting) spherical shell of radius R has a uniform surface charge density...
Problem 5: A thin (non-conducting) spherical shell of radius R has a uniform surface charge density ơ and is spinning around its axis with angular velocity wWo (a) [3 pts] Find the surface current density K of the spinning shell. (b) [5 pts] Find the magnetic dipole moment m of the spinning shell. Some possibly useful integrals: sin3 θd_ (1/12) (cos(39)-9 cos θ) sin' θd_ (1/32)(129-8 sin(29) + sin(40)) sin2 θ cos2 θdθ = (1/32) (49-sin(49) sin'ecosade = (1/30)cos'(9)(3cos(29-7)
There is a circular ring of wire. It has a radius α that carries a current/in a counter clockwise...
There is a circular ring of wire. It has a radius α that carries a current/in a counter clockwise direction. Part A) Reduce equation 10 to find the magnetic field at the center of the loop. Derive this answer from Ampère's Law. Mol R2 10 Part B) Now let's assume it is an insulated circular disk with a uniform charge density σ is spinning at rate o. Utilize Ampère's Law to determine the magnetic field at the center.
There is...
There is a circular ring of wire. It has a radius α that carries a current in a counter clockwise...
There is a circular ring of wire. It has a radius α that carries a current in a counter clockwise direction L.P Part A) Reduce equation 10 to find the magnetic field at the center of the loop. Derive this answer from Ampère's Law Ho R2 401 (cos θ 10 B(z) Part B) Now let's assume it is an insulated circular disk with a uniform charge density σ is spinning at rate ω. Utilize Ampère's Law to determine the magnetic...
A charge is glued on the cylindrical surface of a long circular cylinder of radius R....
A charge
is glued on the cylindrical surface of a long circular cylinder of
radius R. The cylinder is made of a linear dielectric material of
dielectric constant
.
Find the electric field inside the cylinder and show that this
field is uniform.
If a small metal sphere of radius a (a<< R) gets into the
center of the cylinder, find the total dipole moment of the setup
by all charges: free charge, bound charge, and induced charge,
given the...
A circular loop of wire of radius R carries a current I in a region where...
A circular loop of wire of radius R carries a current I in a region where a uniform magnetic field of magnitude B0 is present. (a) If the magnetic dipole moment of the loop makes an angle θ < π/2 with the magnetic field, do a drawing that includes the loop of current, its magnetic dipole moment, the magnetic field, and the direction of the torque experienced by the loop. Make sure to indicate the current i and the angle...
1. *A thin disc of radius a and height h contains charge +q uniformly distributed throughout the disc. The disc lies in...
1. *A thin disc of radius a and height h contains charge +q uniformly distributed throughout the disc. The disc lies in the ry-plane, is located with its centre at the origin, and rotates about the z-axis with angular velocity -w (a) Using cylindrical coordinates (s , z), specify the current density J(s φ z) as a func- tion of position. Find the magnetic dipole moment Hint: After you have determined the volume current density, you can use this result...
1. *A thin disc of radius a and height h contains charge +q uniformly distributed throughout the disc. The disc lies in...
1. *A thin disc of radius a and height h contains charge +q uniformly distributed throughout the disc. The disc lies in the ry-plane, is located with its centre at the origin, and rotates about the z-axis with angular velocity -w (a) Using cylindrical coordinates (s , z), specify the current density J(s φ z) as a func- tion of position. Find the magnetic dipole moment Hint: After you have determined the volume current density, you can use this result...
part b please Consider a rotating disk of radius R with uniform surface charge density sigma...
part b please
Consider a rotating disk of radius R with uniform surface charge density sigma and angular rotation speed omega. (a) show that for an annular strip of radius r, and width dr that the current dI = omega sigma r dr (b) Show that the magnetic field in the center of the disk is given by B = 1/2 mu_0 sigma omega R
A circular disk of radius R=1m has a uniform surface charge density ρS=0.08 μC/m2. The disk...
A circular disk of radius R=1m has a uniform surface charge
density ρS=0.08 μC/m2. The disk lies on the x=0 plane and is
centered at point O(0,0,0).
(2 points) The electric field at the point (2, 6,4) is, in SI units of N/C 10-9 4πε0 E= Introducing a point charge of -100 nC at some point P will make E 0 at the point (2,6,4). Find P. ANSWER: P-(
4. A flat disk of radius R, carrying a uniform charge density + ơ, is rotating at a constant angular velocity o. a) What is the magnitude of the surface current density K at a distance s from the ccnicr f the disk? b) Calculate the magntic field (magnitude and direction) at a point P located on the axis of the disk. [Hint: Treat the disk as a collection of rings of width dr. The current in each ring is...
Problem 5: A thin (non-conducting) spherical shell of radius R has a uniform surface charge density ơ and is spinning around its axis with angular velocity wWo (a) [3 pts] Find the surface current density K of the spinning shell. (b) [5 pts] Find the magnetic dipole moment m of the spinning shell. Some possibly useful integrals: sin3 θd_ (1/12) (cos(39)-9 cos θ) sin' θd_ (1/32)(129-8 sin(29) + sin(40)) sin2 θ cos2 θdθ = (1/32) (49-sin(49) sin'ecosade = (1/30)cos'(9)(3cos(29-7)
There is a circular ring of wire. It has a radius α that carries a current/in a counter clockwise direction. Part A) Reduce equation 10 to find the magnetic field at the center of the loop. Derive this answer from Ampère's Law. Mol R2 10 Part B) Now let's assume it is an insulated circular disk with a uniform charge density σ is spinning at rate o. Utilize Ampère's Law to determine the magnetic field at the center.
There is...
There is a circular ring of wire. It has a radius α that carries a current in a counter clockwise direction L.P Part A) Reduce equation 10 to find the magnetic field at the center of the loop. Derive this answer from Ampère's Law Ho R2 401 (cos θ 10 B(z) Part B) Now let's assume it is an insulated circular disk with a uniform charge density σ is spinning at rate ω. Utilize Ampère's Law to determine the magnetic...
A charge
is glued on the cylindrical surface of a long circular cylinder of
radius R. The cylinder is made of a linear dielectric material of
dielectric constant
.
Find the electric field inside the cylinder and show that this
field is uniform.
If a small metal sphere of radius a (a<< R) gets into the
center of the cylinder, find the total dipole moment of the setup
by all charges: free charge, bound charge, and induced charge,
given the...
1. *A thin disc of radius a and height h contains charge +q uniformly distributed throughout the disc. The disc lies in the ry-plane, is located with its centre at the origin, and rotates about the z-axis with angular velocity -w (a) Using cylindrical coordinates (s , z), specify the current density J(s φ z) as a func- tion of position. Find the magnetic dipole moment Hint: After you have determined the volume current density, you can use this result...
1. *A thin disc of radius a and height h contains charge +q uniformly distributed throughout the disc. The disc lies in the ry-plane, is located with its centre at the origin, and rotates about the z-axis with angular velocity -w (a) Using cylindrical coordinates (s , z), specify the current density J(s φ z) as a func- tion of position. Find the magnetic dipole moment Hint: After you have determined the volume current density, you can use this result...
part b please
Consider a rotating disk of radius R with uniform surface charge density sigma and angular rotation speed omega. (a) show that for an annular strip of radius r, and width dr that the current dI = omega sigma r dr (b) Show that the magnetic field in the center of the disk is given by B = 1/2 mu_0 sigma omega R
A circular disk of radius R=1m has a uniform surface charge
density ρS=0.08 μC/m2. The disk lies on the x=0 plane and is
centered at point O(0,0,0).
(2 points) The electric field at the point (2, 6,4) is, in SI units of N/C 10-9 4πε0 E= Introducing a point charge of -100 nC at some point P will make E 0 at the point (2,6,4). Find P. ANSWER: P-(
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