A 10.0 g block with a charge of +8.00×10-5C is placed in an electric field E = (3000iˆ - 600 ˆj)N /Cs. What are the
(a) magnitude and
(b) direction (relative to the positive direction of the x-axis) of the electrostatic force on the block? If the block is released from rest at the origin at time t = 0, what
are its (c) x and (d) y coordinates at t = 3.00 s?

a) 24.5*10⁻² N b) θ = -11.3º c) x=108 m d) y=-21.6 m

Explanation:

a) Assuming that the block can be treated as a point charge, the electrostatic force on it, must be equal to the product of the electric field, times the value of  the charge.

At the same time, this force must obey Newton's 2nd law, as follows:

F = m*a = q*E

As this is a vector equation, and  we have the value of the x and y components of the electric field, we can decompose it in two algebraic equations, as follows:

Fₓ = m*aₓ = q*Eₓ

Fy = m*ay = q*Ey

In order to find the magnitude of the force F, we can find the magnitude of E, as follows:

The magnitude of the electrostatic force on the block is:

F = q*E = 8.00*10⁻⁵ C * 3.06*10³ N/C =24.5*10⁻² N

b) The direction of the force, as the charge is positive, by convention, is the same as the electric field.

The angle of the electric field with the positive x-axis, can be calculated from the values of Eₓ and Ey, as follows:

θ = tg⁻¹ (Ey/Ex) = tg⁻1 (-600/3000) = tg⁻1 (-.2) = -11.3º (11.3º below horizontal)

c) and d)

As the electric field is uniform, we can get the displacement due to the electrostatic force, applying kinematic equations, to the x and y directions, as they are independent each other due they are perpendicular each other.

As we have already told, we have the following algebraic equations:

Fₓ = m*aₓ = q* Eₓ

Fy = m*ay = q*Ey

As we have the values of Ex, Ey, and m, we can find aₓ and  ay, as follows:

We can find the horizontal and vertical displacements from the origin (the position coordinates at the time t), as follows:

⇒ x, y = 108.0 m, -21.6 m

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

when a device is used in a circuit in which the voltage is 81 v, the current flowing through the device is 3 a. what is the resistance of the device?

a. 27 ω

b. 40.5 a

c. 243 ω

d. 243 a

the correct answer is a. 27