Problems concerning magnetic fields, induced current, emf

[Prototype]

I been trying to work out these problems for the past two days but cannot come up with a solution. If anyone can help that would be greatly appreciated.

1) A 3.80-g bullet moves with a speed of 180m/s perpendicular to the Earth’s magnetic field of 5.00 X 10-5 T. If the bullet possesses a net charge of 8.10 X 10-9 C, by what distance will it be deflected from it’s path do to it’s magnetic field after it has traveled 1.00 km?

2) A galvanometer needle deflects full scale for a 63.0-μA current. What current will give full-scale deflection if the magnetic field weakens to 0.860 of its original value?

3) (a) If the resistance of the resistor in the figure is slowly increased, what is the direction of the current induced in the small circular loop inside the larger loop? (b) What would it be if the small loop were placed outside the larger one, to the left?

 

[Prototype]

Anyone have any ideas?

 

[thepatientmental]

1) To solve this problem, we can use the formula F=qvBsinθ, where F is the magnetic force, q is the charge, v is the velocity, B is the magnetic field, and θ is the angle between the velocity and the magnetic field. In this case, θ=90° because the bullet is moving perpendicular to the magnetic field. Plugging in the values, we get F=(8.10 X 10-9 C)(180 m/s)(5.00 X 10-5 T)sin90°=0.000729 N.

Since the force is perpendicular to the velocity, it will cause the bullet to move in a circular path. We can use the formula F=mv^2/r, where m is the mass, v is the velocity, and r is the radius of the circular path. In this case, we want to find the distance the bullet will be deflected, so we can rearrange the equation to solve for r.

r=mv^2/F=(0.00380 kg)(180 m/s)^2/0.000729 N=11,700 m.

Therefore, the bullet will be deflected by 11,700 m after traveling 1.00 km.

2) To solve this problem, we can use the formula I=μA, where I is the current, μ is the magnetic field, and A is the area of the coil. We know that the initial current, I1, gives full-scale deflection, so we can set up the equation I1=μ1A.

When the magnetic field weakens to 0.860 of its original value, the new current, I2, will give full-scale deflection, so we can set up the equation I2=μ2A.

To find the new current, we can divide the two equations and solve for I2:

I2=I1(μ2/μ1)=63.0 μA(0.860)=54.18 μA.

Therefore, the new current that will give full-scale deflection is 54.18 μA.

3) (a) If the resistance of the resistor is slowly increased, the current in the larger loop will decrease. According to Faraday's law, a changing magnetic field will induce an emf, which will cause a current to flow in the smaller loop. The direction of this induced