29. Sources of Magnetic Field

The current in a wire varies with time according to the relationship $I = 55 A - (0.65 A/s^2)t^2$ . 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 $I=55A-\left(0.65A/s^2\right)t^2$ . How many coulombs of charge pass a cross section of the wire in the time interval between $t=0$ and $t=8.0\text{ s}$?

The total amount of charge in coulombs that has entered a wire at time t is given by the expression Q=4t−t², where t is in seconds and t≥0. 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−t², where t is in seconds and t≥0. 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 $Q=\left(20C\right)(1-e^{-\frac{t}{2.0s}})$, where t is in seconds and t≥0. What is the maximum value of the current?

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. 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?

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.