Answer:
The magnitude of electric field is 22.58 N/C
Solution:
Given:
Force exerted in upward direction, 
Charge, Q = 
Now, we know by Coulomb's law,

Also,
Electric field, 
Thus from these two relations, we can deduce:
F = QE
Therefore, in the question:



Here, the negative side is indicative of the Electric field acting in the opposite direction, i.e., downward direction.
The magnitude of the electric field is:

Answer:
a)
, b) From east to west.
Explanation:
Vectorially, the magnetic force can be calculed by the following formula:

The cross product is:


a) The magnitude of the magnetic force is:

b) The direction of the magnetic force is:
From east to west.
Answer:
A)0.00966 N/C
B) counterclockwise direction
Explanation:
We are given;
Diameter of the metal ring; d = 4.3 cm
Radius;r = 2.15 cm = 0.021- m
Initial magnetic field, B = 1.12 T
Rate of decrease of the magnetic field;dB/dt = 0.23 T/s
Now, as a result of change in magnetic field, an emf will be induced in it. Thus, , electric field is induced and given by the formula :
∫E•dr = d/dt∫B.A •dA
This gives;
E(2πr) = dB/dt(πr²)
Gives;. 2E = dB/dt(r)
E = dB/dt × 2r
We are given;
E = 0.23 × 2(0.021)
E = 0.00966 N/C
The magnitude of the electric field induced in the ring has a magnitude of 0.00966 N/C
B) The direction of electric field will be in a counterclock wise direction when viewed by someone on the south pole of the magnet
Answer:
0.47 N
Explanation:
Here we have a ball in motion along a circular track.
For an object in circular motion, there is a force that "pulls" the object towards the centre of the circle, and this force is responsible for keeping the object in circular motion.
This force is called centripetal force, and its magnitude is given by:

where
m is the mass of the object
is the angular velocity
r is the radius of the circle
For the ball in this problem we have:
m = 40 g = 0.04 kg is the mass of the ball
is the angular velocity
r = 30 cm = 0.30 m is the radius of the circle
Substituting, we find the force:

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