Electricity and Magnetism Answers

 The electric potential in some region in space is given by V (r) = C/r where r = p x 2 + y 2 + z 2 and C is a positive constant. (a) calculate an expression for the electric field in this region. (b) note that ~r = xˆi + ˆj + z ˆk and ~r = rrˆ, express E~ in spherical coordinates. Here ˆr is the radial unit vector of spherical coordinates, sometimes denoted as ˆer. (c) Look and report the expression for the gradient operator in spherical coordinates. Re-derive the expression for E~ , now directly in spherical coordinates.

(a)Derive an expression for VA − VB, the potential difference between points A and B (b) Does your result reduce to the expected answer when d = 0? When a = 0? and when q = 0.

An LC circuit is composed of a 100.0 mH inductor and a 4.0 µF capacitor. If the capacitor can

have a maximum charge of 3.0 µC on its plates,

(a) what is the total energy in the circuit in Joules (J)?

(b) what is the angular frequency of oscillations in the circuit in rads/sec?

(c) what is the maximum current in the circuit in Amperes (A)?

A unicycle has 200 turns of thin wire wrapped around its rim, creating loops with the same

diameter as the wheel. An emf of 9V is induced when the wheel is perpendicular to a magnetic

field that steadily decreases from 0.68 T to 0.24 T in 10 seconds. What is the radius of the

wheel?

A Ferris wheel that can carry almost 100 people has a diameter of 20.0 m. If possible, we

created an electromagnet with 100 coils that can produce a field of an average strength of 0.

90 T parallel to the axis of the wheel. If the field steadily decreases to zero to produce an

induced emf is 50 V, what is the time needed for this induction to happen?

The SkyDome in Toronto, Canada has one of the world’s largest retractable roof. Its area is

32, 000 m2

, and it takes 20 min for the roof to fully retract. If you have a coil wired through the

roof, how many turns do you need to wind up your coil for you to generate an induced emf of

120 V? Assume that a uniform magnetic field with a strength of 3.0 x 10-2 T passes through

the coil parallel to its axis.

A dielectric material of relative dielectric constant 6 is now inserted and completely fills the space between the plate capacitor.Calculate the new chargee

A square loop of wire of side L= 5.0 cm is in a uniform magnetic field B = 0.16 T. What is the magnetic flux in the loop (a) when the magnetic field B is perpendicular to the face of the loop and (b) when B is at an angle of 30° to the area of the loop? (c) What is the magnitude of the average current in the loop if it has a resistance of 0.012Ω and it is rotated from position (b) to position (a) in 0.14 s?

A wire carrying a steady (DC) 30-A current has length L =12 cm between the pole faces of a magnet. The wire is at angle ϴ=600 to the field. The magnetic field is approximately uniform at 0.90 T. We ignore the field beyond the pole pieces. Determine the magnitude and direction of the magnetic force on the wire.