Answer: option 4: A wire that is 2-mm thick and coiled.
Explanation:
The current in each wire is same. The magnetic field due to a current carrying wire increases if the wire is coiled with the more number of turns. A thick wire would cause low resistance to the current. Hence, a 2-mm thick wire which is coiled would produce the strongest magnetic field.
Solution :
a). B at the center :

Here, one of the current is in the clockwise direction and therefore, the other current must be in the clockwise direction in order to cancel out the effect of the magnetic field that is produced by the other.
Therefore, the answer is ANTICLOCKWISE or COUNTERCLOCKWISE
b). Also, the sum of the fields must be zero.
Therefore,

So,


A
Therefore, the current in the outer wire is 24.38 ampere.
Answer:
The angle of banked curve that makes the reliance on friction unnecessary is

Explanation:
In order the car to stay on the curve without friction, the net force in the direction of radius should be equal or smaller than the centripetal force. Otherwise the car could slide off the curve.
The only force in the direction of radius is the sine component of the weight of the car

The cosine component is equivalent to the normal force, which we will not be using since friction is unnecessary.
Newton’s Second Law states that

Also, the car is making a circular motion:

Combining the equations:

Finally the angle is

Answer:
9 and 3 N
Explanation:
Forces in the same direction sum up to produce the resultant force;
One force subtract the other will give the resultant force when they are in opposite directions;
Lets say one direction is forwards and the opposite backwards;
We have one force, let's say force A, in the forwards direction and another force, force B, acting in the same (forwards) or opposite (backwards) direction;
If B is acting in the same direction, then the resultant force (in this case) will be as follows:
A + B = 12
If B is acting in the opposite direction, then the resultant force will be as follows:
A - B = 6
Summing the two equations will allow us to solve for A:
A + B + (A - B) = 12 + 6
2A = 18
A = 9
Substitute this into either of the above equations and we can solve for B:
(9) - B = 6
B = 9 - 6
B = 3