The electric field vec E between two points i | vedclass

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(B) The potential difference between two points in a uniform electric field $\vec E$ is given by $\Delta V = -\int \vec E \cdot d\vec l$. For a unifor

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$Ed \cos 60^o$

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(B) The potential difference between two points in a uniform electric field $\vec E$ is given by $\Delta V = -\int \vec E \cdot d\vec l$. For a uniform electric field,this simplifies to $\Delta V = E \Delta r$,where $\Delta r$ is the displacement along the direction of the electric field. In the given figure,the path length is $d$ at an angle of $60^o$ with the electric field lines. The component of the displacement $d$ along the direction of the electric field is $\Delta r = d \cos 60^o$. Therefore,the potential difference between points $1$ and $2$ is $V = E d \cos 60^o$.

The electric field $\vec E$ between two points is constant in both magnitude and direction. Consider a path of length $d$ at an angle $\theta = 60^o$ with respect to the field lines as shown in the figure. The potential difference between points $1$ and $2$ is

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