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  4. An infinite plane of charge with σ=2 ϵ0 (C/m2) is tilted at a 37° angle to the vertical direction as shown below. Find the potential difference, VA-VB in volts, between points A and B at 5 m distance apart (where B is vertically above A ).

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Q. An infinite plane of charge with $\sigma=2 \epsilon_{0} \frac{C}{m^{2}}$ is tilted at a $37^{\circ}$ angle to the vertical direction as shown below. Find the potential difference, $V_{A}-V_{B}$ in volts, between points $A$ and $B$ at $5\, m$ distance apart (where $B$ is vertically above $A$ ).Physics Question Image

Electrostatic Potential and Capacitance

Solution:

image
$ E =\frac{\sigma}{2 \varepsilon_{0}}=1 \,N / C$
$ \therefore V_{B}-V_{A} $
$=-\int \vec{E} \cdot d \vec{l}=\left(\frac{\sigma}{2 \epsilon_{0}}\right)\left(5 \cos 53^{\circ}\right)=3 \,V$