An object (with charge - 2.4 µC and mass 0.026 kg) hovers at rest above the ground, its weight being held up by a uniform electric field. (a) Find the size and direction of this electric field.

(b) If the electric charge on the object is quadrupled while its mass remains the same, find the size and direction of its acceleration.

a) 10.61 X 10⁴ N/C

b) 29.37 ms⁻².

Explanation:

Since the weight of the object is balanced by force by electric field, the force must be acting in upward direction. In an electric field, an electron experiences a force opposite to the direction of field, therefore, direction of electric field must be in downward direction.

Let E be the electric field. Force on the charge

= electric field x charge = E x 2.4 x 10⁻⁶

Weight acting downwards =.026 x 9.8

For balancing

.026 x 9.8 = E x 2.4 x 10⁻⁶

E =.026 x 9.8 / 2.4 x 10⁻⁶

= 10.61 X 10⁴ N/C

b)

If the charge is quadrupled, charge becomes 4 x 2.4 x 10⁻⁶

Upward force = 4 x 2.4 x 10⁻⁶ x 10.61 X 10⁴ = 101.85 x 10⁻²

Down ward force =.026 x 9.8

Net force = 101.85 x 10⁻² -.026 x 9.8

=.7637 N

acceleration =.7637 /.026 = 29.37 ms⁻².