Charge Moving In A Constant Magnetic Field

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{3}A_{31} Base Sequence = 12735 String Sequence = 12735 - 3 - 31 **

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Charge Moving In A Constant Magnetic Field

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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**:

S_{7}P_{3}A_{31} (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** = q**u** 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.

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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