Final answer:
The strength of the magnetic field can be found by rearranging the relationship between power, emf, current, and resistance in a moving conductor within a magnetic field. The formula to find the magnetic field strength is B = P / (R × l × v^2), where P is power, R is resistance, l is length, and v is velocity. Substituting the given values into this formula and calculating will yield the strength of the magnetic field in teslas (T).
Step-by-step explanation:
To find the strength of the magnetic field given the power dissipation, we first need to relate the power dissipation to the induced current and voltage (emf) in the circuit. When a wire moves perpendicular to a magnetic field with velocity v, an emf (electromotive force) is induced in the wire, which can be calculated using the formula emf = B × l × v, where B is the magnetic field strength, l is the length of the wire, and v is the velocity at which the wire moves.
Since power (P) is the product of current (I) and voltage (V), and V is equal to emf in this scenario, we can write P = I × emf. Because emf = B × l × v, we can also express power as P = I × (B × l × v). Additionally, using Ohm's Law (V = I × R), we know that I = V/R or I = emf/R, where R is the resistance.
Thus, we can rearrange the expression to solve for B as B = P / (l × v × I). Since I = P / (R × v), by substituting I back into the equation, we can find B solely in terms of known quantities: B = P / (R × l × v2). Substituting the given values (P = 4.40 W, R = 0.310Ω, l = 7.00 cm = 0.07 m, and v = 4.00 m/s) into this formula will give us the magnetic field strength, B, in teslas (T).