Suppose there did exist magnetic monopoles. How would you modifyMaxwell's equations and the force law to accommodate them? If you think thereare several plausible options, list them, and suggest how you might decide experimentally which one is right.

Short Answer

Expert verified

The correctly modified Maxwell’s equation isF=α04πqm1qm2r2r^ .

Step by step solution

01

Determine the Maxwell’s equation

Write the Maxwell’s equation.

E=ρÎ0    (Gausslaw)×E=0B=0

Write the amperes law

B=μ0J

02

Determine the right Maxwell’s equation 

As the magnetic monopole exists then there will be no change in Ampere’s law and gauss law.

Actually B=0implies there will be no magnetic monopoles.Then if magnetic monopoles exist, then

B=α0ρm

Hereρm,is the density of magnetic change andα0is the same constant.

Rewrite the Maxwell’s equation as

×E=β0Jm

Here, Jmis the magnetic current density andβ0is another constant.

Thus, magnetic charge is conserved. Hence, ρmandJmsatisfy continuity equation and is written as

Jm+ρmt=0

Write the expression for force on magnetic monopole.

F=qm[B+(υ×E)]

Consider both the equation directionally not correct.

Here, Ehas same units asυB .

Hence, divide υ×Ewith dimensions of velocity squared and rewrite the equation as

F=qe[E+(υ×B)]+qm[B1c2(υ×E)]

Now, write the expression for magnetic field along the lines ofCoulomb’s law.

.

F=α04πqm1qm2r2r^

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Most popular questions from this chapter

A current flows to the right through a rectangular bar of conducting material, in the presence of a uniform magnetic fieldBpointing out of the page (Fig. 5.56).

(a) If the moving charges are positive, in which direction are they deflected by the magnetic field? This deflection results in an accumulation of charge on the upper and lower surfaces of the bar, which in turn produces an electric force to counteract the magnetic one. Equilibrium occurs when the two exactly cancel. (This phenomenon is known as the Hall effect.)

(b) Find the resulting potential difference (the Hall voltage) between the top and bottom of the bar, in terms ofB,v(the speed of the charges), and the relevant dimensions of the bar.23

(c) How would your analysis change if the moving charges were negative? [The Hall effect is the classic way of determining the sign of the mobile charge carriers in a material.]

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