I think you should try. Maxwell himself constructed an elaborate edifice of cogs and mechanisms in space to aid his intuitions about the behaviour of electric and magnetic fields (div and curl). The eponymous equations followed, and his newtonian-physicalist model was thrown away; it took a major cultural shift in physics to accept the validity of equations that seemed to have no intuitive or obvious underlying interpretation.
Of course, modern physics is all like that: no-one has a good intuitive model of Minkowski spacetime, its variably-curved analogue in GR or most particularly for what the equations of quantum mechanics are telling us about 'reality'.
The BBC programme carefully took the lower path, more travelled. But at least they showed Maxwell's equations on a blackboard with a competent professor 'explaining' them to the hapless Stewart. A geologist faced with differential equations! He explained to camera that he understood none of it - he gave a convincing impression of a man whose head hurt.
He could be right. Geologists are, I would guess, less bright than biologists these days ... and how bright are they? Razib Khan had a post about that with this diagram ...
|This diagram is from the science journal Nature|
and this explanation (noting that green is not good) (and also see this):
"The above is from an article in Nature, A test that fails. ...So Professor Stewart, shape up or ship out of this presenting lark!
"My physicist friends always enjoy a chuckle whenever I honestly state that physicists are smarter than biologists, as I am a biologist. There are rare cases, such as Ed Witten, of people entering physics from other fields, but in general it’s the physicists who are the imperialists. And that’s because they’re smart, able to decompose general problems rapidly and decisively. In contrast, biologists are somewhat narrow in their focus, and plodding in their reasoning.
"These are generalizations, but I think they’re roughly correct (I had a friend at a prominent non-profit who was irritated with how difficult it was to find Ph.D. biologists who were flexible thinkers in interviews). And standardized tests bear out my generalization (though honestly, it is a pleasure talking to physicists and mathematicians about out of topic fields compared to biologists partly because they’re so mentally acute; you don’t need GRE stats to get this)."