At a given place the horizontal component of earth's field is 0.2 G. If a vertical wire carries

step 1 In this problem, given that B is equal to 0 .2g, which is equal to 0 .2, multiplication 10 to th

At a given place the horizontal component of earth's field...

At a given place the horizontal component of earth's field is $0.2 \mathrm{G}$. If a vertical wire carries a current of 30 Amp upward, what is the magnitude and direction of the force on 1 meter of wire? (a) $6 \mathrm{E}$ to $\mathrm{W}$ (b) $6 \times 10^{-3} \mathrm{E}$ to $\mathrm{W}$ (c) $6 \times 10^{-3} \mathrm{E}$ to $\mathrm{W}$ (d) $6 \times 10^{-4} \mathrm{E}$ to $\mathrm{W}$

At a given place the horizontal component of earth's field is $0.2 \mathrm{G}$. If a vertical wire carries a current of 30 Amp upward, what is the magnitude and direction of the force on 1 meter of wire?
(a) $6 \mathrm{E}$ to $\mathrm{W}$
(b) $6 \times 10^{-3} \mathrm{E}$ to $\mathrm{W}$
(c) $6 \times 10^{-3} \mathrm{E}$ to $\mathrm{W}$
(d) $6 \times 10^{-4} \mathrm{E}$ to $\mathrm{W}$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Vector Cross Product and Right-Hand Rule

The cross product in the Lorentz force formula determines the direction of the resultant force on a conductor. Using the right-hand rule, one points the fingers in the direction of the current and curls them toward the magnetic field; the thumb then points in the direction of the force. This concept is crucial for predicting the orientation of forces in three-dimensional electromagnetic systems.

Lorentz Force Law

This principle describes the force experienced by a current-carrying conductor when placed in a magnetic field. It is mathematically expressed as F = I (L × B), where I is the current, L is the vector representing the length of the conductor in the direction of current, and B is the magnetic field. This law is fundamental to understanding how magnetic fields interact with moving charges and currents in conductors.

Unit Conversion (Gauss to Tesla)

In many electromagnetic calculations, especially when dealing with Earth's magnetic field, it is essential to convert units from Gauss to Tesla since the SI unit for magnetic field strength is Tesla. The conversion factor is 1 Gauss = 10^(-4) Tesla. This conversion ensures that calculations using standard formulas like the Lorentz force law are consistent and accurate.

Transcript

Please give Ace some feedback