IB Physics HL D 1 9 Hl Potential Gradient Questions

Practise IB Physics HL D.1.9 by calculating gravitational field strength from potential gradients, radial graphs and equipotential spacing.

Exam points

Relate gravitational field strength to the negative spatial gradient of potential.
Estimate g from potential differences across radial distances or equipotential lines.
Interpret the sign and magnitude of a potential gradient in planetary fields.

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Study D.1.9 (HL)—Potential gradient conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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A uniform, spherical planet P has mass M and radius R.

The surface of P is an equipotential surface $E_{0}$ . The dotted circle labeled $E_{1}$ is an equipotential line at a distance $\frac{3 R}{2}$ from the centre of P . The potential difference between $E_{1}$ and $E_{0}$ is $2.2 \times 10^{6} \mathrm{Jkg}^{-1}$ .

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The radius R of P is $8.5 \times 10^{6} \mathrm{~m}$ .

Estimate the magnitude of the gravitational field strength between $E_{1}$ and $E_{0}$ .

$\begin{aligned} g=\pi \frac{\Delta V_{\mathrm{g}}}{\Delta r}=>\frac{2.2 \times 10^{6}}{\frac{8.5 \times 10^{6}}{2}} g=0.52 \ll \mathrm{~N} \mathrm{~kg}^{-1} \gg \end{aligned}$

Ignore negative sign

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IB Physics HL D 1 9 Hl Potential Gradient Questions question 1