# IB DP Physics D.2 Electric and magnetic fields IB Style Question Bank HL Paper 2

### Question

(a) The centres of two identical fixed conducting spheres each of charge $$+Q$$ are separated by a distance $$D$$. C is the midpoint of the line joining the centres of the spheres. (i) Sketch, on the axes, how the electric potential $$V$$ due to the two charges varies with the distance $$r$$ from the centre of the left charge. No numbers are required. Your graph should extend from $$r=0$$ to $$r=D$$. (ii) Calculate the work done to bring a small charge $$q$$ from infinity to point $$C$$.
Data given:
\begin{aligned} & Q=2.0 \times 10^{-3} \mathrm{C}, \\ & q=4.0 \times 10^{-9} \mathrm{C} \\ & D=1.2 \mathrm{~m} \end{aligned}

(b) The small positive charge $$q$$ is placed a distance $$x$$ to the right of $$\mathrm{C}$$. The distance $$x$$ is very small compared to $$D$$. (i) The magnitude of the net force on $$q$$ is given by $$\frac{32 k Q q}{D^3} x$$. Explain why the charge $$q$$ will execute simple harmonic oscillations about $$C$$.

(ii) The mass of the charge $$q$$ is $$0.025 \mathrm{~kg}$$.
Calculate the angular frequency of the oscillations using the data in (a)(ii) and the expression in (b)(i).

(c) The charges $$Q$$ are replaced by neutral masses $$M$$ and the charge $$q$$ by a neutral mass $$m$$. The mass $$m$$ is displaced away from $$C$$ by a small distance $$x$$ and released. Discuss whether the motion of $$m$$ will be the same as that of $$q$$. 

Ans:

Constant, non-zero within spheres
A clear, non-zero positive minimum at $$\mathrm{C} \checkmark$$
Symmetric bowl shaped up curved shape in between $$\checkmark$$

ii \begin{aligned} & V_{\ll}=2 \times \frac{8.99 \times 10^9 \times 2.0 \times 10^{-3}}{0.60} \ggg=6.0 \times 10^7 \& V_» \\ & W=\ll q V=6.0 \times 10^7 \times 4.0 \times 10^{-9}=» 0.24 \ll J »\end{aligned}

b i The restoring force/acceleration is opposite to the displacement/towards equilibrium / OWTTE $$\checkmark$$
and proportional to displacement from equilibrium / OWTTE $$\checkmark$$

ii \begin{aligned} & \omega=\sqrt{\frac{32 k Q q}{m D^3}} \text { OR use of } F=m \omega^2 r \text { OR } F=1.33 \times \text { OR } a=53.3 \times \\ & \kappa=\sqrt{\frac{32 \times 8.99 \times 10^9 \times 2.0 \times 10^{-3} \times 4.0 \times 10^{-9}}{0.025 \times 1.2^3}},=7.299 \ll \mathrm{S}^{-1} w\end{aligned}

c.the net force will no longer be a restoring force/directed towards equilibrium
OR
the gravitational force is attractive/neutral mass would be pulled towards larger masses/OWTTE $$\checkmark$$
«and sow no, motion will not be the same/no longer be SHM / OWTTE $$\checkmark$$

### Question

Two identical positive point charges X and Y are placed 0.30m apart on a horizontal line.
O is the point midway between X and Y. The charge on X and the charge on Y is +4.0µC.

(a) Calculate the electric potential at O.                                                                                                                                              

(b) Sketch, on the axes, the variation of the electric potential V with distance between
X and Y. (c) A positive charge Z is released from rest 0.010m from O on the line between X and Y.
Z then begins to oscillate about point O. (i) Identify the direction of the resultant force acting on Z as it oscillates.                                                                              

(ii) Deduce whether the motion of Z is simple harmonic.  