A conducting straight wire of length 20 cm is moving with a constant speed of 5 m/s perpendicular to uniform 0.2 T magnetic field. The wire is perpendicular to the magnetic field. Calculate the voltage across the wire.
In this problem we need to use an expression for the induced voltage across the moving wire in uniform magnetic field. The voltage is given by the following expression E = B*L*v B=0.2T L=20cm=0.2m v= 5 m/s E=0.2*0.2*5 = 0.2 v
Prove the identity (1 + cos(x) + cos(2x)) / (sin(x) + sin(2x)) = cot(x)
Use the identities cos(2x) = 2 cos2(x) - 1 and sin(2x) = 2 sin(x) cos(x) in the left hand side of the given identity. [ 1 + cos(x) + cos(2x) ] / [ sin(x) + sin(2x) ] = [ 1 + cos(x) + 2 cos2(x) - 1 ] / [ sin(x) + 2 sin(x) cos(x) ] = [ cos(x) + 2 cos2(x) ] / [ sin(x) + 2 sin(x) cos(x) ] = cos(x) [1 + 2 cos(x)] / [ sin(x)( 1 + 2 cos(x) ) ] = cot(x)
Find the equation of the line that passes through the points (-1 , -1) and (-1 , 2).
To find the equation of the line through the points (-1 , -1) and (-1 , 2), we first use the slope m. m = (y2 - y1) / (x2 - x1) = (2 - -1) / (-1 - -1) = 3 / 0 The slope is indefined which means the line is perpendicular to the x axis and its equation has the form x = constant. Since both points have equal x coordinates -1, the equation is given by: x = -1