Question

In a region, the electric potential varies as V = 10 − 50x, where V is in volts and x in meters. The electric field in the region is ______.

Options

• 10 N/C along +x.

• 10 N/C along −x.

• 50 N/C along +x.

• 50 N/C along −x.

Answer 1

In a region, the electric potential varies as V = 10 − 50x, where V is in volts and x in meters. The electric field in the region is 50 N/C along +x.

Explanation:

The electric potential V is given as a function of the spatial coordinate x:

V(x) = 10 − 50x

The electric field E is defined as the negative gradient of the electric potential V. For a one-dimensional variation along the x-axis, the relationship is:

E_x = `-(dV)/dx`

Differentiate the potential function with respect to x:

`(dV)/dx = d/dx(10 - 50x)`

= 0 − 50

= − 50 V/m

Substitute the derivative back into the electric field formula:

E_x = −(−50)

= 50 V/m

Since 1 V/m = 1 N/C, the magnitude is 50 N/C. Because the value is positive, the field vector points in the positive x direction.

∴ The electric field in the region is 50 N/C along +x.