Question

The Electric Potential of the Earth The Earth has a vertical electric field with a magnitude of approximately 100 V/m near its surface.

What is the magnitude of the potential difference between a point on the ground and a point on the same level as the top of the Washington Monument (555 ft high)?

Answer 1

The magnitude of the potential difference between the ground and the top of the Washington Monument, which is 555 feet or approximately 169.164 meters tall, caused by Earth's electric field of about 100 V/m, is roughly 16,916.4 volts.

Step-by-step explanation:

The question refers to calculating the electric potential difference caused by Earth's electric field. The provided value of Earth's electric field is approximately 100 V/m near its surface. To find the potential difference (ΔV) between a point on the ground and a point at the height of the top of the Washington Monument, we can use the equation:

ΔV = E * d

where E is the electric field strength and d is the distance in meters. Since the height of the Washington Monument is given in feet, it needs to be converted to meters (1 foot = 0.3048 meters). The height in meters is:

555 ft * 0.3048 m/ft = 169.164 m

Now, we can calculate the potential difference:

ΔV = 100 V/m * 169.164 m = 16916.4 V

Thus, the magnitude of the potential difference between a point on the ground and a point at the level of the top of the Washington Monument is approximately 16,916.4 volts.

Answer 2

16916.4 V

Step-by-step explanation:

Electric potential: This is the work done in bringing a unit positive charge from infinity to that point in against the action of the field. The S.I unit of Electric potential is V.

mathematically, Electric potential can be expressed as

P = E×d ....................................... Equation 1.

Where P = Electric potential, E = Electric Field, d = distance/height of the level at the top of the Washington Monument.

Given: E = 100 V/m, d = 555 ft = 555×0.3048 m = 169.164 m.

Substitute into equation 1

P = 100×169.164

P = 16916.4 V.

Thus the potential difference = 16916.4 V.