A uniform electric field \( \vec E \) points along +X. Point A is at the origin, B at (1 cm, 0), and C at (0, 1 cm). Which relation between their potentials is correct?
Potential drops along the field direction and remains constant on any plane perpendicular to \( \vec E \).
Well done. Since \(V\) decreases along +X, the origin is at a higher potential than point B.
Recall that \(V\) falls in the field direction and is unchanged perpendicular to it. Try again.
Two conducting spheres of radii r1 and r2 are joined by a thin wire and kept far apart. After they reach common potential, what is the ratio of the surface electric fields \( |E_1| : |E_2| \)?
At equilibrium \( V=\dfrac{kq}{r} \) on both spheres, so \( E=\dfrac{kq}{r^{2}}\propto\dfrac{1}{r} \).
Well done! Equal potential gives \(E\propto1/r\); therefore \(E_{1}/E_{2}=r_{2}/r_{1}\).
Recall that connecting conductors equalises their potentials, leading to \(E\propto1/r\). Try again!
A long straight wire of radius a carries uniform current I. Compare the magnetic field magnitude at (i) a point a / 2 inside the wire and (ii) a point a / 2 outside the surface. Choose the correct ratio (outside : inside).
Inside: \(B=\mu_0 I r / (2\pi a^2)\). Outside: \(B=\mu_0 I / (2\pi r)\). Use \(r=0.5a\) and \(1.5a\), then form the ratio \(B_{out}:B_{in}\).
Well done! \(B_{out}/B_{in}=4/3\) because \(B\propto r\) inside the wire and \(B\propto 1/r\) outside.
Revisit the Ampere’s law expressions for inside and outside points and substitute the given radii.
The diffraction effect can be observed in:
Diffraction appears when wavefronts meet an opening or obstacle comparable in size to their wavelength.
Diffraction is a universal wave phenomenon. Both audible sound and visible light bend around openings—e.g., sound heard around a corner and light fringes at a razor edge.
Remember: any wave bends when its wavelength is comparable to the size of the opening. Re-evaluate each option with this idea.
Uniform E lowers potential along +X: VA < VB; along Y it is unchanged, so VA = VC.
At equilibrium E ∝ 1/r, therefore E1:E2 = r2:r1.
Using Ampere’s law at ±a/2, magnetic field ratio (outside : inside) is 4 : 3.
Diffraction occurs when aperture ≈ λ, so all waves qualify. Next, practise with Questions 5–8.