An alpha particle(the nucleus of a helium atom) has a mass of 6.64*10^-27kg and a charge of +2e. What are the magnitude and direction of the electric field that will balance the gravitational force on it? Mp= 1.67*10^-27kg
To find the magnitude and direction of the electric field that will balance the gravitational force on an alpha particle, we need to equate these two forces and solve for the electric field.
1. Set up the equation of force balance:
Electric force = Gravitational force
The electric force is given by:
Fe = qe * E
The gravitational force is given by:
Fg = mg
Here, Fe is the electric force, qe is the charge of the alpha particle, E is the electric field, Fg is the gravitational force, m is the mass of the alpha particle, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. Substitute the given values:
Fe = qe * E
Fg = mg
The charge of an alpha particle is +2e (where e is the elementary charge = 1.6 x 10^-19 C), and the mass of the alpha particle (mp) is 6.64 x 10^-27 kg.
Therefore, the equations become:
Fe = (2e) * E
Fg = (6.64 x 10^-27 kg) * (9.8 m/s^2)
3. Set the electric force equal to the gravitational force:
(2e) * E = (6.64 x 10^-27 kg) * (9.8 m/s^2)
4. Solve for E:
E = [(6.64 x 10^-27 kg) * (9.8 m/s^2)] / (2e)
Calculate this expression to find the value of E.
5. Substitute the values into the equation:
E = [(6.64 x 10^-27 kg) * (9.8 m/s^2)] / (2 * 1.6 x 10^-19 C)
Calculate this expression to find the value of E.
The magnitude of the electric field is the absolute value of E, and the direction of the electric field is the same as the direction of the positive charge (+2e).
To find the magnitude and direction of the electric field that will balance the gravitational force on the alpha particle, we need to equate the two forces and solve for the electric field.
The gravitational force acting on the alpha particle is given by the equation:
F_gravity = m * g
Where:
m = mass of the alpha particle = 6.64 * 10^-27 kg
g = acceleration due to gravity = 9.8 m/s^2
F_gravity = (6.64 * 10^-27 kg) * (9.8 m/s^2)
F_gravity = 6.5072 * 10^-26 N
The electric force acting on the alpha particle is given by the equation:
F_electric = q * E
Where:
q = charge of the alpha particle = +2e
e = elementary charge = 1.6 * 10^-19 C
E = electric field
F_electric = (+2e) * E
F_electric = (2 * 1.6 * 10^-19 C) * E
F_electric = 3.2 * 10^-19 E
Now, we can equate the gravitational force and electric force:
6.5072 * 10^-26 N = 3.2 * 10^-19 E
To solve for E, we divide both sides by 3.2 * 10^-19:
E = (6.5072 * 10^-26 N) / (3.2 * 10^-19)
E = 2.027 * 10^-7 N/C
So, the magnitude of the electric field that will balance the gravitational force on the alpha particle is 2.027 * 10^-7 N/C.
Since the charge on the alpha particle is positive, the electric field must be pointing opposite to the gravitational force. Therefore, the direction of the electric field is upward.