29. Sources of Magnetic Field

As a proton passes the origin, its velocity is $3.0\times {10}^5\mathrm{m}/\mathrm{s}$in the positive x direction. What is the magnitude of the magnetic field at the point ($12.0\mathrm{cm}$, $5.0\mathrm{cm}$, $0.0\mathrm{cm}$)?

As a proton passes the origin, its velocity is $3.0\times {10}^5\mathrm{m}/\mathrm{s}$ in the positive x direction. What is the direction of the magnetic field at the point ($12.0\mathrm{cm}$, $5.0\mathrm{cm}$, $0.0\mathrm{cm}$)?

A charged particle moving in a magnetic field has a force to the top of the page when it is moving toward the right and the field is into the page. Is this particle positive, negative or neutral?

What is the force on an electron with velocity $\stackrel{\rightharpoonup }{v}=(3.0\times {10}^5\frac{\mathit{m}}{\mathit{s}})\widehat{i}+(4.0\times {10}^5\frac{\mathit{m}}{\mathit{s}})\widehat{k}$ in a region of space with magnetic field $\stackrel{\rightharpoonup }{B}=(2.4\times {10}^{-4}\mathit{T})\widehat{i}$?

The circuit shown in Fig. E25.33

contains two batteries, each with an emf and an internal resistance, and two resistors. Find (b) the terminal voltage Vab of the 16.0-V battery

The circuit shown in Fig. E25.33

contains two batteries, each with an emf and an internal resistance, and two resistors. Find (a) the current in the circuit (magnitude and direction)

The current in a wire varies with time according to the relationship I = 55 A - (0.65 A/s^2)t^2. (b) What constant current would transport the same charge in the same time interval?

The current in a wire varies with time according to the relationship I = 55 A - (0.65 A/s^2)t^2 . (a) How many coulombs of charge pass a cross section of the wire in the time interval between t = 0 and t = 8.0 s? (b) What constant current would transport the same charge in the same time interval?

An idealized ammeter is connected to a battery as shown in Fig. E25.28

. Find (c) the terminal voltage of the battery.

An idealized ammeter is connected to a battery as shown in Fig. E25.28

. Find (b) the current through the 4.00-Ω resistor.

An idealized ammeter is connected to a battery as shown in Fig. E25.28

. Find (a) the reading of the ammeter.

The total amount of charge in coulombs that has entered a wire at time t is given by the expression Q=4t−t^2, where t is in seconds and t≥0. a. Find an expression for the current in the wire at time .

The total amount of charge in coulombs that has entered a wire at time t is given by the expression Q=4t−t^2, where t is in seconds and t≥0. b. Graph I versus t for the interval 0≤t≤4 s.

The total amount of charge that has entered a wire at time t is given by the expression Q=(20 C)(1−e−ᵗ/⁽².⁰ ˢ⁾, where t is in seconds and t≥0. b. What is the maximum value of the current?

The current supplied by a battery slowly decreases as the battery runs down. Suppose that the current as a function of time is I=(0.75 A)e−ᵗ/⁽⁶ ʰ⁾. What is the total number of electrons transported from the positive electrode to the negative electrode by the charge escalator from the time the battery is first used until it is completely dead?

A 5.0-mm-diameter proton beam carries a total current of 1.5 mA. The current density in the proton beam, which increases with distance from the center, is given by J=Jₑdgₑ(r/R) , where R is the radius of the beam and Jₑdgₑ is the current density at the edge. b. Determine the value of Jₑdgₑ.

A circuit you're building needs an ammeter that goes from 0 mA to a full-scale reading of 50 mA. Unfortunately, the only ammeter in the storeroom goes from 0 μA to a full-scale reading of only 500 μA. Fortunately, you've just finished a physics class, and you realize that you can make this ammeter work by putting a resistor in parallel with it, as shown in FIGURE P28.56. You've measured that the resistance of the ammeter is 50.0 Ω, not the 0 Ω of an ideal ammeter. b. What is the effective resistance of your ammeter?

Compared to an ideal battery, by what percentage does the battery's internal resistance reduce the potential difference across the 20 Ω resistor in FIGURE EX28.24?

a. Load resistor R is attached to a battery of emf and internal resistance r. For what value of the resistance R, in terms of ∈ and r, will the power dissipated by the load resistor be a maximum?

A 2.0-m-long, 1.0-mm-diameter wire has a variable resistivity given by where x is measured from one end of the wire. What is the current if this wire is connected to the terminals of a 9.0 V battery?

A proton moves along the x-axis with vₓ = 1.0 x 10⁷ m/s.. As it passes the origin, what are the strength and direction of the magnetic field at the (x, y, z) positions (a) (1 cm, 0 cm, 0 cm), (b) (0 cm, 1 cm, 0 cm), and (c) (0 cm, -2 cm, 0 cm)?

What is the magnetic field at the position of the dot in FIGURE EX29.6? Give your answer as a vector.