An electric field of 200 V/m exists in the region between the places of the parallel plate capacitor of plate separation 5 cm.(a) Find the potential difference between the plates when a slab of dielectric constant 4 and thickness 1 cm is inserted parallel to plates. (b)The slab is now replaced by a metal plate of thickness x cm.Find the value of x such that the potential difference between the plates remains the same as in case (a)

Dear student,

We call the quantity the gradient of the electric potential in the -direction. It basically measures how fast the potential varies as the coordinate is changed (but the coordinates and are held constant). Thus, the above formula is saying that the -component of the electric field at a given point in space is equal to minus the local gradient of the electric potential in the -direction.

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