Vector Force Exerted On A Charge Moving In A Constant Magnetic Field
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Vector Force Exerted On A Charge Moving In A Constant Magnetic Field

Figure 1.2 shows a charge q moving with velocity u (a vector) in a magnetic field with magnetic flux density B (a vector). Assuming that the field is a scalar field (i.e, it is spatially unidirectional).
(a) Express the vector force f in terms of the charge q, and the vectors u and B.
(b) What is the magnitude of f If u makes an angle θ with the magnetic field?
(c) Suppose the magnetic flux lines are perpendicular to a cross sectional area A (fig1.3). Express the magnetic flux ψ, of the field in terms of the flux density B.

(d) State Faraday's Law that relate magnetic flux φ to eletromotive force (emf), e.

The string:
S7P3A31 (Force - Pull).
The math:

Pj Problem of interest is of type force. The force a magnetic field exert can be a pull or a push. Force-push is exerted in a field where repulsion is dominant while force-pull is exerted a field where attraction is dominant.
Magnetic fields are generated by electric charge in motion. Their effect is measured by the force they exert on a moving charge.

(a) Vector force, f = qu x B ------(1)
Where the symbol x in equation (1) is a cross product.

(b) Magnitude of vector force = |f| = q|u||B|sinθ = quBsinθ

(c) The magnetic flux φ is expressed as an integral as follows:

Where φ is in webers and the integral subscript A indicates that the integration is over the surface area, A.
When the magnetic flux is uniform over the cross sectional area, A; the integral could be approximated as follows:
φ = B.A (i.e., the flux density B multiplied by the cross sectional area, A).

(d) Faraday's Law of induction states that voltage and therefore current is induced in a conductor in a changing magnetic field.
In other words, a time-varying flux causes an induced electromotive force (emf), e as follows:
e = dφ/dt.

Blessed are they that have not seen, and yet have believed. John 20:29

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