Suppose a 7kg bob is hanging from the ceiling in a region with uniform electric field E= 46x + 29y N/C. Find the charge on the bob if it's angular position is displaced from the vertical by 20 degrees.

To find the charge on the bob, we need to use the concept of electrostatic force and gravitational force.

The electrical force on a charged object in an electric field is given by the equation:

F = q * E

Where F is the force, q is the charge on the object, and E is the electric field intensity.

In this case, the electrical force is acting in the opposite direction to the gravitational force.

The gravitational force on the bob is given by the equation:

F_gravity = m * g

Where F_gravity is the gravitational force, m is the mass of the bob, and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Since the bob is displaced from the vertical by 20 degrees, we can decompose the gravitational force into two components: one parallel to the electric field and one perpendicular to it.

The perpendicular component is responsible for the tension in the string, while the parallel component cancels out with the electrical force.

The perpendicular component of the gravitational force is given by:

F_perpendicular = m * g * sin(theta)

Where theta is the angle of displacement from the vertical (20 degrees in this case).

Now, equating the electrical force and the perpendicular component of the gravitational force:

q * E = F_perpendicular

q * E = m * g * sin(theta)

Plugging in the given values:

E = 46x + 29y N/C,
m = 7 kg,
g = 9.8 m/s^2,
theta = 20 degrees.

We substitute the values and solve for q:

q * (46x + 29y) = 7 * 9.8 * sin(20 degrees)

Now we can calculate the value of q by dividing both sides of the equation by (46x + 29y):

q = (7 * 9.8 * sin(20 degrees)) / (46x + 29y)

Therefore, the charge on the bob is (7 * 9.8 * sin(20 degrees)) / (46x + 29y).